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PARABOLIC FREQUENCY MONOTONICITY FOR TWO NONLINEAR EQUATIONS UNDER RICCI FLOW 认领 引用
1
作者 Chuanhuan LI Yi LI +1 位作者 Kairui XU Jichun ZHU 《Acta Mathematica Scientia》 SCIE CSCD 2026年第2期752-766,共15页
In this paper,we study the parabolic frequency for positive solutions of two nonlinear parabolic equations under the Ricci flow on closed manifolds.The first equation is■tu=Δg(t)u+au+|▽g(t)u|2 with a co... In this paper,we study the parabolic frequency for positive solutions of two nonlinear parabolic equations under the Ricci flow on closed manifolds.The first equation is■tu=Δg(t)u+au+|▽g(t)u|2 with a constant a;the other one is ■tu=Δg(t)u+λup with two constantsλand p≥1.Here g(t)is the Riemannian metric involved by Ricci flow.We establish the monotonicity of the parabolic frequency for the solutions of two nonlinear parabolic equations with bounded Ricci curvature.Subsequently,we apply the parabolic frequency monotonicity to derive some integral type Harnack inequalities.Additionally,we use−K1 instead of the lower bound 0 of Ricci curvature from Theorem 1.3 in[16],where K1 is any positive constant.This is a preview of subscription content,log in via an institution to check access. 展开更多
关键词 Ricci flow parabolic frequency nonlinear equation
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SOLVERS FOR SYSTEMS OF LARGE SPARSE LINEAR AND NONLINEAR EQUATIONS BASED ON MULTI-GPUS 认领 引用 被引量：3
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作者 刘沙 钟诚文 陈效鹏 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2011年第3期300-308,共9页
Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremend... Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremendous time due to the extremely large size encountered in most real-world engineering applications.So,practical solvers for systems of linear and nonlinear equations based on multi graphic process units（GPUs）are proposed in order to accelerate the solving process.In the linear and nonlinear solvers,the preconditioned bi-conjugate gradient stable（PBi-CGstab）method and the Inexact Newton method are used to achieve the fast and stable convergence behavior.Multi-GPUs are utilized to obtain more data storage that large size problems need. 展开更多
关键词 general purpose graphic process unit（GPGPU） compute unified device architecture（CUDA） system of linear equations system of nonlinear equations Inexact Newton method bi-conjugate gradient stable（Bi-CGstab）method
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A Nonmonotone Trust Region Method for Solving Symmetric Nonlinear Equations 认领 引用 被引量：3
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作者 YUAN Gong-lin WEI Zeng-xin LU Xi-wen 《Chinese Quarterly Journal of Mathematics》 2009年第4期574-584,共11页
A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical res... A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems. 展开更多
关键词 trust region method nonlinear equations nonmonotone technique
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THE MAPPING RELATION AMONG SOLUTION OF SOME NONLINEAR EQUATIONS 认领 引用 被引量：1
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作者 倪光炯 楼森岳 《Acta Mathematica Scientia》 SCIE 1989年第2期131-141,共11页
Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of... Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two. 展开更多
关键词 DSG THE MAPPING RELATION AMONG SOLUTION OF SOME NONLINEAR EQUATIONS
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On Newton-Like Methods for Solving Nonlinear Equations 认领 引用 被引量：1
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作者 KOU Jisheng LIU Dingyou LI Yitian HE Julin 《Geo-Spatial Information Science》 EI 2006年第1期76-78,共3页
In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treat... In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treated. The methods are proved to be quadratically convergent provided the w eak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative meth ods with a variable parameter are developed. 展开更多
关键词 Newton method Newton-like method nonlinear equations iteration method
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A weak condition for secant method to solve systems of nonlinear equations 认领 引用
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作者 LIANG Ke-wei HAN Dan-fu +1 位作者 ZHANG Hong ZHU Cheng-yan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2009年第1期90-96,共7页
In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x0 is replaced by that with xl, the first approximat... In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x0 is replaced by that with xl, the first approximation generated by the secant method with the initial data x-1 and x0. Under the bounded conditions of the divided difference, a convergence theorem is obtained and two examples to illustrate the weakness of convergence conditions are provided. Moreover, the secant method is applied to a system of nonlinear equations to demonstrate the viability and effectiveness of the results in the paper. 展开更多
关键词 secant method Banach space radius of convergence systems of nonlinear equations complexity
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ANALYTICAL FORMULAS OF SOLUTIONS OF GEOMETRICALLY NONLINEAR EQUATIONS OF AXISYMMETRIC PLATES AND SHALLOW SHELLS 认领 引用
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作者 Zheng Xiaojing Zhou Youhe, Department of Mechanics, Lanzhou University 《Acta Mechanica Sinica》 SCIE CAS 1990年第1期69-80,共12页
Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence... Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equa- tions. 展开更多
关键词 circular thin plates and shallow shells axisymmetric deformation nonlinear equations exact solution analytical formulas
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Efficient Numerical Scheme for Solving Large System of Nonlinear Equations 认领 引用 被引量：1
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作者 Mudassir Shams Nasreen Kausar +2 位作者 Shams Forruque Ahmed Irfan Anjum Badruddin Syed Javed 《Computers, Materials & Continua》 SCIE EI 2023年第3期5331-5347,共17页
A fifth-order family of an iterative method for solving systems of nonlinear equations and highly nonlinear boundary value problems has been developed in this paper.Convergence analysis demonstrates that the local ord... A fifth-order family of an iterative method for solving systems of nonlinear equations and highly nonlinear boundary value problems has been developed in this paper.Convergence analysis demonstrates that the local order of convergence of the numerical method is five.The computer algebra system CAS-Maple,Mathematica,or MATLAB was the primary tool for dealing with difficult problems since it allows for the handling and manipulation of complex mathematical equations and other mathematical objects.Several numerical examples are provided to demonstrate the properties of the proposed rapidly convergent algorithms.A dynamic evaluation of the presented methods is also presented utilizing basins of attraction to analyze their convergence behavior.Aside from visualizing iterative processes,this methodology provides useful information on iterations,such as the number of diverging-converging points and the average number of iterations as a function of initial points.Solving numerous highly nonlinear boundary value problems and large nonlinear systems of equations of higher dimensions demonstrate the performance,efficiency,precision,and applicability of a newly presented technique. 展开更多
关键词 Nonlinear equations convergence order boundary value problem computational time basins of attraction converging points
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Dynamical Comparison of Several Third-Order Iterative Methods for Nonlinear Equations 认领 引用 被引量：2
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作者 Obadah Said Solaiman Samsul Ariffin Abdul Karim Ishak Hashim 《Computers, Materials & Continua》 SCIE EI 2021年第5期1951-1962,共12页
There are several ways that can be used to classify or compare iterative methods for nonlinear equations,for instance;order of convergence,informational efficiency,and efficiency index.In this work,we use another way,... There are several ways that can be used to classify or compare iterative methods for nonlinear equations,for instance;order of convergence,informational efficiency,and efficiency index.In this work,we use another way,namely the basins of attraction of the method.The purpose of this study is to compare several iterative schemes for nonlinear equations.All the selected schemes are of the third-order of convergence and most of them have the same efficiency index.The comparison depends on the basins of attraction of the iterative techniques when applied on several polynomials of different degrees.As a comparison,we determine the CPU time(in seconds)needed by each scheme to obtain the basins of attraction,besides,we illustrate the area of convergence of these schemes by finding the number of convergent and divergent points in a selected range for all methods.Comparisons confirm the fact that basins of attraction differ for iterative methods of different orders,furthermore,they vary for iterative methods of the same order even if they have the same efficiency index.Consequently,this leads to the need for a new index that reflects the real efficiency of the iterative scheme instead of the commonly used efficiency index. 展开更多
关键词 Nonlinear equations iterative methods basins of attraction order of convergence
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Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems 认领 引用 被引量：1
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作者 Aijuan Song Guohua Wu +1 位作者 Witold Pedrycz Ling Wang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2022年第1期75-89,共15页
Nonlinear equations systems(NESs)are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots.Evolutionary algorithms(EAs)are one of the methods for solving NESs,... Nonlinear equations systems(NESs)are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots.Evolutionary algorithms(EAs)are one of the methods for solving NESs,given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run.Currently,the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs.By contrast,problem domain knowledge of NESs is investigated in this study,where we propose the incorporation of a variable reduction strategy(VRS)into EAs to solve NESs.The VRS makes full use of the systems of expressing a NES and uses some variables(i.e.,core variable)to represent other variables(i.e.,reduced variables)through variable relationships that exist in the equation systems.It enables the reduction of partial variables and equations and shrinks the decision space,thereby reducing the complexity of the problem and improving the search efficiency of the EAs.To test the effectiveness of VRS in dealing with NESs,this paper mainly integrates the VRS into two existing state-of-the-art EA methods(i.e.,MONES and DR-JADE)according to the integration framework of the VRS and EA,respectively.Experimental results show that,with the assistance of the VRS,the EA methods can produce better results than the original methods and other compared methods.Furthermore,extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance. 展开更多
关键词 Evolutionary algorithm(EA) nonlinear equations systems(ENSs) problem domain knowledge variable reduction strategy(VRS)
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A new variable coefficient algebraic method and non-travelling wave solutions of nonlinear equations 认领 引用 被引量：14
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作者 陆斌 张鸿庆 《Chinese Physics B》 SCIE EI CAS 2008年第11期3974-3984,共11页
In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than pr... In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations. 展开更多
关键词 nonlinear partial differential equations non-travelling wave solutions asymmetric Nizhnik-Novikov- Vesselov equation
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Design Principles-Based Interactive Learning Tool for Solving Nonlinear Equations 认领 引用
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作者 Ahad Alloqmani Omimah Alsaedi +2 位作者 Nadia Bahatheg Reem Alnanih Lamiaa Elrefaei 《Computer Systems Science & Engineering》 SCIE EI 2022年第3期1023-1042,共20页
Interactive learning tools can facilitate the learning process and increase student engagement,especially tools such as computer programs that are designed for human-computer interaction.Thus,this paper aims to help s... Interactive learning tools can facilitate the learning process and increase student engagement,especially tools such as computer programs that are designed for human-computer interaction.Thus,this paper aims to help students learn five different methods for solving nonlinear equations using an interactive learning tool designed with common principles such as feedback,visibility,affordance,consistency,and constraints.It also compares these methods by the number of iterations and time required to display the result.This study helps students learn these methods using interactive learning tools instead of relying on traditional teaching methods.The tool is implemented using the MATLAB app and is evaluated through usability testing with two groups of users that are categorized by their level of experience with root-finding.Users with no knowledge in root-finding confirmed that they understood the root-finding concept when interacting with the designed tool.The positive results of the user evaluation showed that the tool can be recommended to other users. 展开更多
关键词 Graphical user interface(GUI) interactive learning tool design principles nonlinear equations experimental design
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Different-Periodic Travelling Wave Solutions for Nonlinear Equations 认领 引用 被引量：1
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作者 YELi-Jun LINJi 《Communications in Theoretical Physics》 SCIE CAS 2004年第4期481-486,共6页
Using Jacobi elliptic function linear superposition approach for the (1+1)-dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation and the (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equation, many ne... Using Jacobi elliptic function linear superposition approach for the (1+1)-dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation and the (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equation, many new periodic travelling wave solutions with different periods and velocities are obtained based on the known periodic solutions. This procedure is crucially dependent on a sequence of cyclic identities involving Jacobi elliptic functions sn(), cn(), and dn(). 展开更多
关键词 linear superposition nonlinear equation travelling wave solution
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Envelope Periodic Solutions to Coupled Nonlinear Equations 认领 引用 被引量：1
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作者 LIUShi－Da FuZun－Tao 《Communications in Theoretical Physics》 SCIE CAS 2003年第2期167-172,共6页
The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate t... The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate tothe envelope shock wave solutions and/or the envelope solitary wave solutions. 展开更多
关键词 Jacobi elliptic function nonlinear coupled equations envelope periodic solution
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A Maple Package on Symbolic Computation of Hirota Bilinear Form for Nonlinear Equations 认领 引用 被引量：1
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作者 YANG Xu-Dong RUAN Hang-Yu 《Communications in Theoretical Physics》 SCIE CAS 2009年第11期801-807,共7页
An improved algorithm for symbolic computation of Hirota bilinear forms of KdV-type equations withlogarithmic transformations is presented.In the algorithm,the general assumption of Hirota bilinear form is successfull... An improved algorithm for symbolic computation of Hirota bilinear forms of KdV-type equations withlogarithmic transformations is presented.In the algorithm,the general assumption of Hirota bilinear form is successfullyreduced based on the property of uniformity in rank.Furthermore,we discard the integral operation in the traditionalalgorithm.The software package HBFTrans is written in Maple and its running effectiveness is tested by a variety solitonequations. 展开更多
关键词 Hirota bilinear form nonlinear equation,symbolic algebra
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On a Class of Solitary Wave Solutions of Atmospheric Nonlinear Equations 认领 引用
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作者 R. Dhar C. Guha-Roy D. K. Sinha 《Advances in Atmospheric Sciences》 SCIE CAS 1991年第3期357-362,共6页
In this paper, an attempt is made to study some interesting results of the coupled nonlinear equations in the atmosphere. By introducing a phase angle function ζ, it is shown that the atmospheric equations in the pre... In this paper, an attempt is made to study some interesting results of the coupled nonlinear equations in the atmosphere. By introducing a phase angle function ζ, it is shown that the atmospheric equations in the presence of specific forcing exhibit the exact and explicit solitary wave solutions under certain conditions. 展开更多
关键词 On a Class of Solitary Wave Solutions of Atmospheric Nonlinear Equations
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Extended Hyperbola Function Method and Its Application to Nonlinear Equations 认领 引用 被引量：1
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作者 HUANGDing-Jiang ZHANGHong-Qing 《Communications in Theoretical Physics》 SCIE CAS 2004年第6期801-804,共4页
An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be f... An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics. 展开更多
关键词 nonlinear wave equations exact solitary wave solution hyperbola function method
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Construction of solitonary and periodic solutions to some nonlinear equations using EXP-function method 认领 引用
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作者 ZHANG Mei ZHANG Wen-jing 《Journal of Zhejiang University-SCIENCE A》 SCIE EI CAS 2007年第4期660-664,共5页
This paper applies the EXP-function method to find exact solutions of various nonlinear equations. Tzitzeica- Dodd-Bullough (TDB) equation was selected to illustrate the effectiveness and convenience of the suggested ... This paper applies the EXP-function method to find exact solutions of various nonlinear equations. Tzitzeica- Dodd-Bullough (TDB) equation was selected to illustrate the effectiveness and convenience of the suggested method. More generalized solitonary solutions with free parameters were obtained by suitable choice of the free parameters, and also the obtained solitonary solutions can be converted into periodic solutions. 展开更多
关键词 Soliton Periodic solution Nonlinear equation EXP-function method
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A NOTE ON PROBABILISTIC CONTRACTOR COUPLE AND SOLUTIONS FOR A SYSTEM OF NONLINEAR EQUATIONS IN N A MENGER PN-SPACES 认领 引用
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作者 方锦暄 宋桂安 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第7期841-848,共8页
The concept of (Phi, Delta)-type probabilistic contractor couple was introduced which simplifies and weakens the definition of probabilistic contractor couple given by Zhang Shisheng. The existence and uniqueness of t... The concept of (Phi, Delta)-type probabilistic contractor couple was introduced which simplifies and weakens the definition of probabilistic contractor couple given by Zhang Shisheng. The existence and uniqueness of the solutions for a system of nonlinear operator equations with this kind of propabilistic contractor couple in N. A. Menger PN-spaces were studied. The works improve and extend the corresponding results by M. Altman, A. C. Lee, W. J. Padgett et al. 展开更多
关键词 N. A. Menger PN-space (Phi, Delta)-probabilistic contractor couple selective operator nonlinear operator equations
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A COMPLETE BOUNDARY INTEGRAL FORMULATION FOR STEADY COMPRESSIBLE INVISCID FLOWS GOVERNED BY NONLINEAR EQUATIONS 认领 引用
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作者 Yang Zuo-sheng Nanjing Aeronautical Institute 《Chinese Journal of Aeronautics》 EI CAS 1991年第4期333-338,共6页
A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced ... A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain. 展开更多
关键词 A COMPLETE BOUNDARY INTEGRAL FORMULATION FOR STEADY COMPRESSIBLE INVISCID FLOWS GOVERNED BY NONLINEAR EQUATIONS PV
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