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HIGH ORDER PROBABILISTIC NUMERICAL METHODS FOR FORWARD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS 认领 引用
1
作者 Qiang Han Yurong Liu 《Journal of Computational Mathematics》 SCIE CSCD 2026年第6期1631-1661,共31页
In this paper,we design novel high order probabilistic numerical algorithms for forward backward stochastic differential equations.Moreover,we derive the error estimates and prove the high order convergence rates of t... In this paper,we design novel high order probabilistic numerical algorithms for forward backward stochastic differential equations.Moreover,we derive the error estimates and prove the high order convergence rates of the proposed schemes.Because the proposed scheme involves conditional expectations,an estimator based on the multilevel Monte Carlo method is applied to approximate the conditional expectations.Furthermore,we theoretically demonstrate that the computational complexity of our numerical method is proportional to the square of prescribed accuracy.Numerical experiments are given to illustrate the theoretical results. 展开更多
关键词 Forward Backward Stochastic Differential Equation Probabilistic Numerical Method Multilevel Monte Carlo Computational Complexity High Order Discretization
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An efficient and accurate numerical method for simulating close-range blast loads of cylindrical charges based on neural network 认领 引用 被引量：3
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作者 Ting Liu Changhai Chen +2 位作者 Han Li Yaowen Yu Yuansheng Cheng 《Defence Technology（防务技术）》 SCIE EI CAS CSCD 2025年第2期257-271,共15页
To address the problems of low accuracy by the CONWEP model and poor efficiency by the Coupled Eulerian-Lagrangian(CEL)method in predicting close-range air blast loads of cylindrical charges,a neural network-based sim... To address the problems of low accuracy by the CONWEP model and poor efficiency by the Coupled Eulerian-Lagrangian(CEL)method in predicting close-range air blast loads of cylindrical charges,a neural network-based simulation(NNS)method with higher accuracy and better efficiency was proposed.The NNS method consisted of three main steps.First,the parameters of blast loads,including the peak pressures and impulses of cylindrical charges with different aspect ratios(L/D)at different stand-off distances and incident angles were obtained by two-dimensional numerical simulations.Subsequently,incident shape factors of cylindrical charges with arbitrary aspect ratios were predicted by a neural network.Finally,reflected shape factors were derived and implemented into the subroutine of the ABAQUS code to modify the CONWEP model,including modifications of impulse and overpressure.The reliability of the proposed NNS method was verified by related experimental results.Remarkable accuracy improvement was acquired by the proposed NNS method compared with the unmodified CONWEP model.Moreover,huge efficiency superiority was obtained by the proposed NNS method compared with the CEL method.The proposed NNS method showed good accuracy when the scaled distance was greater than 0.2 m/kg1/3.It should be noted that there is no need to generate a new dataset again since the blast loads satisfy the similarity law,and the proposed NNS method can be directly used to simulate the blast loads generated by different cylindrical charges.The proposed NNS method with high efficiency and accuracy can be used as an effective method to analyze the dynamic response of structures under blast loads,and it has significant application prospects in designing protective structures. 展开更多
关键词 Close-range air blast load Cylindrical charge Numerical method Neural network CEL method CONWEP model
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Multi-Phase Modeling for Vulnerability Detection & Patch Management: An Analysis Using Numerical Methods 认领 引用
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作者 Adarsh Anand Div ya +1 位作者 Deepti Aggrawal Omar H.Alhazmi 《Computers, Materials & Continua》 SCIE EI 2025年第7期1529-1544,共16页
Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implemen... Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implementation,or configuration.To guarantee the durability&robustness of the software,vulnerability identification and fixation have become crucial areas of focus for developers,cybersecurity experts and industries.This paper presents a thorough multi-phase mathematical model for efficient patch management and vulnerability detection.To uniquely model these processes,the model incorporated the notion of the learning phenomenon in describing vulnerability fixation using a logistic learning function.Furthermore,the authors have used numerical methods to approximate the solution of the proposed framework where an analytical solution is difficult to attain.The suggested systematic architecture has been demonstrated through statistical analysis using patch datasets,which offers a solid basis for the research conclusions.According to computational research,learning dynamics improves security response and results in more effective vulnerability management.The suggested model offers a systematic approach to proactive vulnerability mitigation and has important uses in risk assessment,software maintenance,and cybersecurity.This study helps create more robust software systems by increasing patch management effectiveness,which benefits developers,cybersecurity experts,and sectors looking to reduce security threats in a growing digital world. 展开更多
关键词 Learning phenomenon numerical method patching two-phase modelling vulnerability
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A Review of the Numerical Methods for Diblock Copolymer Melts 认领 引用
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作者 Youngjin Hwang Seungyoon Kang Junseok Kim 《Computers, Materials & Continua》 SCIE EI 2025年第2期1811-1838,共28页
This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form c... This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form complex structures at the nanometer scale and play a significant role in various applications.The phase-field model,in particular,is essential for describing the formation and evolution of these structures and is widely used as a tool to effectively predict the movement of phase boundaries and the distribution of phases over time.In this paper,we discuss the principles and implementations of various numerical methodologies for this model and analyze the strengths,limitations,stability,accuracy,and computational efficiency of each method.Traditional approaches such as Fourier spectral methods,finite difference methods and alternating direction explicit methods are reviewed,as well as recent advancements such as the invariant energy quadratization method and the scalar auxiliary variable scheme are also presented.In addition,we introduce examples of the phase-field model,which are fingerprint image restoration and 3D printing.These examples demonstrate the extensive applicability of the reviewed methods and models. 展开更多
关键词 Nonlocal cahn–hilliard phase-field diblock copolymer melts Ohta–Kawasaki model numerical methods pattern formation
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FFT-Based Numerical Method for Nonlinear Elastic 认领 引用 被引量：3
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作者 Fei Guo Fan Wu +2 位作者 Xinyong Li Yijie Huang Zhuo Wang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2023年第5期266-279,共14页
In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic co... In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplifed to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the fnite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efciency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplifed numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications. 展开更多
关键词 Numerical method Elastoplastic contact Hyperelastic contact FEM FFT
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Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape.Part II:Numerical Methods and Test Experiments 认领 引用 被引量：6
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作者 CAO Jie Qin XU 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2011年第6期1445-1458,共14页
Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary(around a data hole)inside the domain,the... Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary(around a data hole)inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes(grid-staggering,local-nesting and piecewise continuous integration)are designed to deal with the singularity of the Green's function encountered in numerical calculations.For the externally induced part,by setting the velocity potential(or streamfunction)component to zero,the other component of the solution can be computed in two ways:(1)Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.(2)Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting(or piecewise continuous integration),the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point(or along the entire boundary).When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others. 展开更多
关键词 numerical method streamfunction velocity potential domain of arbitrary shape
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Numerical method of studying nonlinear interactions between long waves and multiple short waves 认领 引用 被引量：1
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作者 谢涛 旷海兰 +5 位作者 William Perrie 邹光辉 南撑峰 何超 沈涛 陈伟 《Chinese Physics B》 SCIE EI CAS 2009年第7期3090-3098,共9页
Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we ... Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train （expressed as wave train 2） leads to the energy focusing of the other short wave train （expressed as wave train 3）. This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3. 展开更多
关键词 sea surface nonliear interaction numerical method
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A numerical method for determining the stuck point in extended reach drilling 认领 引用 被引量：2
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作者 Sun Lianzhong Gao Deli 《Petroleum Science》 SCIE CAS CSCD 2011年第3期345-352,共8页
A stuck drill string results in a major non-productive cost in extended reach drilling engineering.The first step is to determine the depth at which the sticking has occurred.Methods of measurement have been proved us... A stuck drill string results in a major non-productive cost in extended reach drilling engineering.The first step is to determine the depth at which the sticking has occurred.Methods of measurement have been proved useful for determining the stuck points,but these operations take considerable time.As a result of the limitation with the current operational practices,calculation methods are still preferred to estimate the stuck point depth.Current analytical methods do not consider friction and are only valid for vertical rather than extended reach wells.The numerical method is established to take full account of down hole friction,tool joint,upset end of drill pipe,combination drill strings and tubular materials so that it is valid to determine the stuck point in extended reach wells.The pull test,torsion test and combined test of rotation and pulling can be used to determine the stuck point.The results show that down hole friction,tool joint,upset end of drill pipe,tubular sizes and materials have significant effects on the pull length and/or the twist angle of the stuck drill string. 展开更多
关键词 Extended reach drilling stuck pipe torque and drag numerical method
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The Application of Barr Numerical Method to Realize Abel Inversion 认领 引用 被引量：2
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作者 田崇利 周艳 《Plasma Science and Technology》 SCIE EI CAS 2006年第5期521-523,共3页
An 8-channel HCN laser interferometer will be installed on HL-2A in near term. In order to get the spatial profile of the electron density Barr numerical method is adopted to realize the Abel inversion. In this articl... An 8-channel HCN laser interferometer will be installed on HL-2A in near term. In order to get the spatial profile of the electron density Barr numerical method is adopted to realize the Abel inversion. In this article the result of the Abel inversion by Matlab GUI is given which can be updated to process the measured data of the 8-channel laser interferometer and provide the spatial distribution of the electron density. 展开更多
关键词 Abel inversion Barr numerical method Matlab GUI
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Numerical Method for Modeling the Constitutive Relationship of Sand under Different Stress Paths 认领 引用 被引量：5
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作者 Ren Qingyang Wang Jingtao 《Journal of China University of Geosciences》 2005年第3期268-270,共3页
A numerical method was used in order to establish the constitutive relationship of sands under different stress paths, Firstly, based on the numerical method modeling the constitutive law of sands, the elastoplastic c... A numerical method was used in order to establish the constitutive relationship of sands under different stress paths, Firstly, based on the numerical method modeling the constitutive law of sands, the elastoplastic constitutive relationship of sand was established for three paths： the constant proportion of principle stress path, the conventional triaxial compression （CTC） path, and the p=constant （TC） path. The yield lines of plastic volumetric strain and plastic generalized shear strain were given. Through visualization, the three dimensional surface of the stress-strain relationship in the whole stress field （p, q） obtained under the three paths was plotted. Also, by comparing the stress-strain surfaces and yield locus of the three stress paths, the differences were found to be obvious, which demonstrates that the influence of the stress paths on constitutive law was not neglected. The numerical modeling method overcame the difficulty of finding an analytical expression for plastic potential. The results simulated the experimental data with an accuracy of 90% on average, so the constitutive model established in this paper provides an effective constitutive equation for this kind of engineering, reflecting the effect of practical stress paths that occur in sands. 展开更多
关键词 constitutive relationship numerical method modeling stress path
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A two scaled numerical method for global analysis of high dimensional nonlinear systems 认领 引用 被引量：1
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作者 Jun Jiang 《Theoretical & Applied Mechanics Letters》 EI CAS 2011年第6期45-50,共6页
This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems,which regard state space respectively as continuous and discrete ones.On basis of this unde... This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems,which regard state space respectively as continuous and discrete ones.On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference(PMUCR),has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems,which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them.The basic ideas and main steps of implementation of the two scaled method,namely extended PMUCR,are elaborated.Finally,two examples are presented to demonstrate the capabilities of the proposed method. 展开更多
关键词 nonlinear systems global analysis multi-scaled numerical methods point mapping cell mapping point mapping under cell reference
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Hybrid numerical method for wall-resolved large-eddy simulations of compressible wall-bounded turbulence 认领 引用
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作者 Ming Yu Yalu Fu +3 位作者 Pengxin Liu Zhigong Tang Xianxu Yuan Chunxiao Xu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2022年第9期64-76,共13页
In the present study,we propose a hybrid numerical method for wall-resolved large-eddy simulation of compressible wall-bounded turbulence.Based on the hierarchical feature of energetic structures in wall-bounded turbu... In the present study,we propose a hybrid numerical method for wall-resolved large-eddy simulation of compressible wall-bounded turbulence.Based on the hierarchical feature of energetic structures in wall-bounded turbulence,we propose to solve the convective term in the near-wall region with the low-dissipative kinetic energy preserving scheme to resolve the small-scale structures and the upwind scheme away from the wall to avoid strong numerical oscillations generated by the spurious errors.Two parameters are introduced in this method,one related to the transition point y+p and the other the transition rangeα.By a series of well-designed test cases,we identify that setting y+p as the streamwise grid intervalΔx+gives the best results,whereas the effects of the variation ofαare marginal.By further performing simulations at higher Reynolds numbers and Mach numbers,we prove that the presently proposed method is capable of accurately predicting the skin friction,mean velocity and temperature and velocity fluctuation intensities and,in the meantime,retaining numerical stability. 展开更多
关键词 Hybrid numerical method Large-eddy simulation Compressible wall-bounded turbulence
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A baroclinic typhoon model with a moving multi-nested grid and variational adjustment initialisationI. Numerical method 认领 引用
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作者 Wu Huiding Yang Xuelian Bai Shan and Li Guoqing 1. National Marine Environmental Forecasting Centre, State Oceanic Administration, Beijing 100081, China 2. Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’ s, 《Acta Oceanologica Sinica》 SCIE CAS 1999年第2期191-201,共11页
A baroclinic typhoon model with a moving multi--nested grid is applied in marine environmental forecasts. This paper describes the numerical methods of the model including governing equations, finite differencing, spl... A baroclinic typhoon model with a moving multi--nested grid is applied in marine environmental forecasts. This paper describes the numerical methods of the model including governing equations, finite differencing, split scheme and time integration. 展开更多
关键词 Typhoon model 3-dimensional baroclinic numerical method moving nested grid
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A NUMERICAL METHOD FOR FRACTIONAL INTEGRAL WITH APPLICATIONS 认领 引用
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作者 朱正佑 李根国 程昌钧 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第4期373-384,共12页
A new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated. The method can be used to solve the integro_differential equation includin... A new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated. The method can be used to solve the integro_differential equation including fractional integral or fractional derivative in a long history. The difficulty of storing all history data is overcome and the error can be controlled. As application,motion equations governing the dynamical behavior of a viscoelastic Timoshenko beam with fractional derivative constitutive relation are given. The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables method. Then the new numerical method is used to solve a class of weakly singular Volterra integro_differential equations which are applied to describe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmerical results are compared. It is found that they are very close. 展开更多
关键词 fractional calculus numerical method fractional derivative constitutive relation weakly singular Volterra integro_differential equation
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Numerical method of Rayleigh-Stokes problem for heated generalized second grade fluid with fractional derivative 认领 引用
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作者 庄平辉 刘青霞 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第12期1533-1546,共14页
In this paper,we consider the Rayleigh-Stokes problem for a heated generalized second grade fluid（RSP-HGSGF）with fractional derivative.An effective numerical method for approximating RSP-HGSGF in a bounded domain is... In this paper,we consider the Rayleigh-Stokes problem for a heated generalized second grade fluid（RSP-HGSGF）with fractional derivative.An effective numerical method for approximating RSP-HGSGF in a bounded domain is presented.The stability and convergence of the method are analyzed.Numerical examples are presented to show the application of the present technique. 展开更多
关键词 Rayleigh-Stokes problem numerical method stability convergence
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A NUMERICAL METHOD OF K-S ENTROPY CALCULATION FOR A STRANGE ATTRACTOR 认领 引用
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作者 赵南 刘曾荣 《Acta Mechanica Sinica》 SCIE CAS 1992年第1期16-20,共5页
Based directly on the original definition of K-S entropy, a new algorithm for calculating K-S entropy from chaotic time series is developed by using some techniques of coding and code operation.
关键词 chaos K-S entropy numerical method coding
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A High-Order Conservative Numerical Method for Gross-Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC 认领 引用
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作者 李翔 钱旭 +1 位作者 唐玲艳 宋松和 《Chinese Physics Letters》 SCIE EI CAS CSCD 2017年第6期5-9,共5页
We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-or... We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions. 展开更多
关键词 A High-Order Conservative Numerical Method for Gross-Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC
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NUMERICAL METHOD FOR SOLVING THE EULER EQUATION FOR UNSTEADY TRANSONIC FLOWS OVER OSCILLATING AIRFOILS 认领 引用
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作者 Li FengweiNorthwestern Polytechnical University 《Chinese Journal of Aeronautics》 EI CAS 1991年第1期1-10,共10页
Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be ... Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be satisfied exactly without increasing the computational time. The novel scheme is useful for computing transonic, strong disturbance, unsteady flows with high reduced frequencies. The scheme makes use of curvefitted orthogonal meshes and the lattice control technique to obtain the optimal grid distribution. The numerical results are satisfactory. 展开更多
关键词 NUMERICAL METHOD FOR SOLVING THE EULER EQUATION FOR UNSTEADY TRANSONIC FLOWS OVER OSCILLATING AIRFOILS Flow NACA
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Analysis profile of the fully grouted rock bolt in jointed rock using analytical and numerical methods 认领 引用 被引量：9
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作者 Ghadimi Mostafa Shahriar Kourosh Jalalifar Hossein 《International Journal of Mining Science and Technology》 EI CAS 2014年第5期609-615,共7页
The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods.Based on the analytical method with dev... The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods.Based on the analytical method with development of methods,a new model is presented.To validate the analytical model,five different profiles modeled by ANSYS software.The profile of rock bolts T3 and T4with load transfer capacity,respectively 180 and 195 kN in the jointed rocks was selected as the optimum profiles.Finally,the selected profiles were examined in Tabas Coal Mine.FLAC analysis indicates that patterns 6+7 with2 NO flexi bolt 4 m better than other patterns within the faulted zone. 展开更多
关键词 Fully grouted bolt Load transfer mechanism Jointed rocks Analytical and numerical methods
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An Effective Numerical Method for the Solution of a Stochastic Coronavirus(2019-nCovid)Pandemic Model 认领 引用 被引量：5
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作者 Wasfi Shatanawi Ali Raza +3 位作者 Muhammad Shoaib Arif Kamaledin Abodayeh Muhammad Rafiq Mairaj Bibi 《Computers, Materials & Continua》 SCIE EI 2021年第2期1121-1137,共17页
Nonlinear stochastic modeling plays a significant role in disciplines such as psychology,finance,physical sciences,engineering,econometrics,and biological sciences.Dynamical consistency,positivity,and boundedness are ... Nonlinear stochastic modeling plays a significant role in disciplines such as psychology,finance,physical sciences,engineering,econometrics,and biological sciences.Dynamical consistency,positivity,and boundedness are fundamental properties of stochastic modeling.A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation.Well-known explicit methods such as Euler Maruyama,stochastic Euler,and stochastic Runge–Kutta are investigated for the stochastic model.Regrettably,the above essential properties are not restored by existing methods.Hence,there is a need to construct essential properties preserving the computational method.The non-standard approach of finite difference is examined to maintain the above basic features of the stochastic model.The comparison of the results of deterministic and stochastic models is also presented.Our proposed efficient computational method well preserves the essential properties of the model.Comparison and convergence analyses of the method are presented. 展开更多
关键词 Coronavirus pandemic model stochastic ordinary differential equations numerical methods convergence analysis
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