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Numerical Methods for Boundary Value Problems in Variable Coefficient Ordinary Differential Equations 认领 引用 被引量：1
1
作者 ZHAO Ting-ting CAI Wei-yun 《Chinese Quarterly Journal of Mathematics》 2025年第3期295-303,共9页
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error... In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation. 展开更多
关键词 Variable coefficient ordinary differential equations Lagrange interpolation Difference methods
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SECOND-ORDER ACCURATE DIFFERENCE METHOD FOR THE SINGULARLY PERTURBED PROBLEM OF FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS 认领 引用
2
作者 王国英 陈明伦 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第5期463-468,共6页
In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.
关键词 SECOND-ORDER ACCURATE DIFFERENCE METHOD FOR THE SINGULARLY PERTURBED PROBLEM OF FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS
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THE GROWTH OF DIFFERENCE EQUATIONS AND DIFFERENTIAL EQUATIONS 认领 引用 被引量：2
3
作者 Zongxuan CHEN Ranran ZHANG +1 位作者 Shuangting LAN Chuangxin CHEN 《Acta Mathematica Scientia》 SCIE CSCD 2021年第6期1911-1920,共10页
In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential equations.We delete the condition(1.6)of Theorems E... In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential equations.We delete the condition(1.6)of Theorems E and F,yet obtain the same results for Theorems E and F.We also weaken the condition(1.4)of Theorems C and D. 展开更多
关键词 asymptotic Method difference equations differential equations
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Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems 认领 引用 被引量：1
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作者 Chunlei Ruan Cengceng Dong +2 位作者 Zeyue Zhang Boyu Chen Zhijun Liu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第9期2707-2728,共22页
Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using t... Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions. 展开更多
关键词 Peridynamic differential operator finite difference method stability transient heat conduction problem
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Buckling analysis of nanobeams with exponentially varying stiffness by differential quadrature method 认领 引用 被引量：1
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作者 S Chakraverty Laxmi Behera 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第7期218-227,共10页
We present the application of differential quadrature（DQ） method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler-Bernoulli, Timoshenko, Redd... We present the application of differential quadrature（DQ） method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler-Bernoulli, Timoshenko, Reddy, and Levison.The formulation is based on the nonlocal elasticity theory of Eringen. New results are presented for the guided and simply supported guided boundary conditions. Numerical results are obtained to investigate the effects of the nonlocal parameter,length-to-height ratio, boundary condition, and nonuniform parameter on the critical buckling load parameter. It is observed that the critical buckling load decreases with increase in the nonlocal parameter while the critical buckling load parameter increases with increase in the length-to-height ratio. 展开更多
关键词 differential quadrature method exponentially varying stiffness different beam theories
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Application of Mixed Differential Quadrature Method for Solving the Coupled Two-Dimensional Incompressible Navier-Stokes Equation and Heat Equation 认领 引用 被引量：2
6
作者 A.S.J.AL-SAIF 朱正佑 《Journal of Shanghai University(English Edition)》 2003年第4期343-351,共9页
The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. T... The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. The new method was compared with theconventional differential quadrature method in the aspects of convergence and accuracy. The resultsshow that the new method is more accurate, and has better convergence than the conventionaldifferential quadrature method for numerically computing the steady-state solution. 展开更多
关键词 coupled N-S equation and heat equation differential quadrature method upwind difference scheme
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Novel Multisoliton-Like Solutions of the Differential-Difference KdV Equation 认领 引用 被引量：8
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作者 杜丛民 邓淑芳 孙梅娜 《Journal of Shanghai University(English Edition)》 2004年第2期134-137,共4页
This article is concerned with the Hirota direct method for studying novel multisoliton solutions of the discrete KdV equation. First the Hirota method was introduced, then the novel multisoliton solutions were obtain... This article is concerned with the Hirota direct method for studying novel multisoliton solutions of the discrete KdV equation. First the Hirota method was introduced, then the novel multisoliton solutions were obtained. Simultaneously the figures of the novel one-soliton solution and two-soliton solution were given and the singularity of the novel multisoliton solutions was discussed. Finally it was pointed out that the multisoliton solutions with sigularity can only be called soliton-like solutions. Key words differential-difference KdV equation - Hirota method - multisoliton-like solutions MSC 2000 35Q51 Project supported by the National Natural Science Foundation of China(Grant No. 19571052) 展开更多
关键词 differential-difference KdV equation Hirota method multisoliton-like solutions
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An Introduction to Numerical Methods for the Solutions of Partial Differential Equations 认领 引用 被引量：3
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作者 Manoj Kumar Garima Mishra 《Applied Mathematics》 2011年第11期1327-1338,共12页
Partial differential equations arise in formulations of problems involving functions of several variables such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity, etc. The... Partial differential equations arise in formulations of problems involving functions of several variables such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity, etc. The present paper deals with a general introduction and classification of partial differential equations and the numerical methods available in the literature for the solution of partial differential equations. 展开更多
关键词 Partial Differential Equations Eigenvalue Finite Difference Method Finite Volume Method Finite Element Method
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Application of the Hybrid Differential Transform Method to the Nonlinear Equations 认领 引用
9
作者 Inci Cilingir Sungu* Huseyin Demir 《Applied Mathematics》 2012年第3期246-250,共5页
In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform... In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform and finite differences, are used in different subdomains. Our aim of this approach is to combine the flexibility of differential transform and the efficiency of finite differences. An explicit hybrid method for the transient response of inhomogeneous nonlinear partial differential equations is presented;applying finite difference scheme on the fixed grid size is used to approximate the space discretisation, whereas the differential transform method is used for time operator. Comparison of the efficiency of the different approaches is a very important aspect of this study. In our test cases, the hybrid approach is faster than the corresponding highly optimized finite difference method in two dimensional computations. We compared our hybrid approach’s results with the exact and/or numerical solutions of PDE which obtained from Adomian Decomposition Method. Results show that the hybrid approach may be an important tool to reduce the execution time and memory requirements for large scale computations and get remarkable results in predicting the solutions of nonlinear initial value problems. 展开更多
关键词 Hybrid Differential Transform/Finite Difference Method Nonlinear Initial Value Problems Numerical Solution
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ON THE ARBITRARY DIFFERENCE PRECISE INTEGRATION METHOD AND ITS NUMERICAL STABILITY 认领 引用
10
作者 强士中 王孝国 +1 位作者 唐茂林 刘民 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第3期269-275,共7页
Based on the subdomain precise integration method, the arbitrary difference precise integration method (ADPIM) is presented to solve PDEs. While retaining all the merits of the former method, ADPIM further demonstrate... Based on the subdomain precise integration method, the arbitrary difference precise integration method (ADPIM) is presented to solve PDEs. While retaining all the merits of the former method, ADPIM further demonstrates advantages such as the abilities of better description of physical properties of inhomogeneous media and convenient treatment of various boundary conditions. The explicit integration schemes derived by ADPIM are proved unconditionally stable. 展开更多
关键词 partial differential equations difference method numerical stability
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THE NUMERICAL SOLUTION OF A SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR PARABOLIC DIFFERENTIAL EQUATION 认领 引用
11
作者 苏煜城 沈全 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第11期1047-1056,共10页
The numerical solution of a singularly perturbed problem for the semilinear parabolic differential equation with parabolic boundary layers is discussed. A nonlinear two-level difference scheme is constructed on the sp... The numerical solution of a singularly perturbed problem for the semilinear parabolic differential equation with parabolic boundary layers is discussed. A nonlinear two-level difference scheme is constructed on the special non-uniform grids. The uniform con vergence of this scheme is proved and some numerical examples are given. 展开更多
关键词 semilinear parabolic differential equation singularly perturbed problem finite difference method uniform convergence
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Furnace Temperature Curve Optimization Model Based on Differential Evolution Algorithm 认领 引用 被引量：1
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作者 Yiming Cheng 《Journal of Electronic Research and Application》 2024年第4期64-80,共17页
When soldering electronic components onto circuit boards,the temperature curves of the reflow ovens across different zones and the conveyor belt speed significantly influence the product quality.This study focuses on ... When soldering electronic components onto circuit boards,the temperature curves of the reflow ovens across different zones and the conveyor belt speed significantly influence the product quality.This study focuses on optimizing the furnace temperature curve under varying settings of reflow oven zone temperatures and conveyor belt speeds.To address this,the research sequentially develops a heat transfer model for reflow soldering,an optimization model for reflow furnace conditions using the differential evolution algorithm,and an evaluation and decision model combining the differential evolution algorithm with the Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)method.This approach aims to determine the optimal furnace temperature curve,zone temperatures of the reflow oven,and the conveyor belt speed. 展开更多
关键词 Furnace temperature curve Difference equations Differential evolution algorithms TOPSIS methods
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On the Arbitrary Difference Precise Integration Method and Its Numerical Stability 认领 引用
13
作者 刘浪 王孝国 强士中 《Journal of Modern Transportation》 2000年第1期51-58,共8页
Based on the subdomain precise integration method, the arbitrary difference precise integration method (ADPIM) is presented to solve PDEs. While retaining all the merits of the former method, ADPIM also demonstrates a... Based on the subdomain precise integration method, the arbitrary difference precise integration method (ADPIM) is presented to solve PDEs. While retaining all the merits of the former method, ADPIM also demonstrates advantages such as the abilities of better description of physical properties of inhomogeneous media and convenient treatment of various boundary conditions. The explicit integration schemes derived by ADPIM are proved unconditionally stable. 展开更多
关键词 partial differential equations difference method numerical stability
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SINE TRANSFORM PRECONDITIONERS FOR SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS 认领 引用
14
作者 金小庆 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 1993年第1期116-123,共8页
In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the ... In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale. 展开更多
关键词 Sine Transform finite difference method second-order partial differential equation condition number preconditioned conjugate gradient method
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Convergence analysis for the Secant method based on new recurrence relations 认领 引用 被引量：1
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作者 BI Wei-hong REN Hong-min WU Qing-biao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE 2008年第4期447-454,共8页
A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided differenc... A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works. 展开更多
关键词 Secant method Banach space recurrence relation semilocal convergence Lipschitz continuous divided difference
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Second-order difference scheme for a nonlinear model of wood drying process 认领 引用
16
作者 姜明杰 孙志忠 《Journal of Southeast University(English Edition)》 EI CAS 2006年第4期582-588,共7页
A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordin... A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result. 展开更多
关键词 wood drying process model nonlinear differential equation difference scheme method of reduction of order stability convergence
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从分子到临床:抑郁症异质性的中西医多维解析与个体化治疗策略研究进展 认领 引用 被引量：1
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作者 田佳雪 秦雪梅 刘晓节 《中国药理学通报》 CAS CSCD 北大核心 2026年第2期207-216,共10页
由于抑郁患者个体体质、生活环境等不同,且常伴有不同兼杂之症,故在临床表现及药物疗效评价方面呈现明显差异。常用抗抑郁药物易引起脑出血、勃起功能障碍、停药反应、自杀意念和行为风险增加等严重不良反应。这些均提示抑郁症在发病机... 由于抑郁患者个体体质、生活环境等不同,且常伴有不同兼杂之症,故在临床表现及药物疗效评价方面呈现明显差异。常用抗抑郁药物易引起脑出血、勃起功能障碍、停药反应、自杀意念和行为风险增加等严重不良反应。这些均提示抑郁症在发病机制、临床表现、药效等方面存在异质性。该文基于中西医理论,全面分析和总结了抑郁症不同分型及给药后个体差异,并深入探讨了其不同发病机制,强调了研究抑郁症异质性对患者个体化治疗的不可或缺性。此外,该文还总结了抑郁症不同阶段中西医用药策略,为患者科学、详细评估提供指导,为伴有不同症状的患者提供用药建议,为抑郁症机制的深入、全面阐释提供理论依据,为中西医结合、中西药联用的临床策略的制定提供方向。 展开更多
关键词 抑郁症 异质性 不良反应 同病异治 辨证论治 中西药联用
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基于非靶向代谢组学分析不同月龄岗巴绵羊血清代谢物差异 认领 引用
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作者 李杨 牛惠冬 +7 位作者 徐茂胜 韩文祥 张立 汪亚苹 吴玉江 次仁曲珍 李明 许会芬 《基因组学与应用生物学》 CAS CSCD 北大核心 2026年第1期108-118,共11页
岗巴绵羊(Ovis aries)生长于低氧低压的高海拔地区,其生长发育过程伴随着复杂的代谢调控。本研究旨在通过非靶向代谢组学技术比较不同月龄岗巴绵羊的血清代谢物差异,以期动态地揭示岗巴绵羊生长过程中血清代谢物的动态变化规律,并筛选... 岗巴绵羊(Ovis aries)生长于低氧低压的高海拔地区,其生长发育过程伴随着复杂的代谢调控。本研究旨在通过非靶向代谢组学技术比较不同月龄岗巴绵羊的血清代谢物差异,以期动态地揭示岗巴绵羊生长过程中血清代谢物的动态变化规律,并筛选出潜在的生长标志物及关键代谢通路。随机选取自然放牧条件下的6(M6)、18(M18)、36(M36)及48(M48)月龄的健康去势岗巴绵羊公羊各3只为试验对象,采集血清后进行非靶向代谢组学测序分析。结果表明,不同月龄岗巴绵羊血清代谢谱存在差异。其中,在M6 vs M18、M18 vs M36、M36 vs M48分析组中分别鉴定到90、23、32种差异代谢物(VIP大于1,P<0.05)。进一步分析发现,M6 vs M18分析组的90种差异代谢物中的上调及下调差异代谢物分别有14种及76种,M18 vs M36分析组的23种差异代谢物中具有显著性上调、下调差异代谢物分别有11、12种,M36 vs M48分析组的32种差异代谢物中的显著性上调、下调差异代谢物分别有22、10种。差异代谢物主要包括甘油磷脂类和氨基酸。L-缬氨酸、L-谷氨酰胺、Bovinic acid等血清代谢物在不同月龄岗巴绵羊血清中波动变化。KEGG富集分析显示,不同月龄岗巴绵羊的差异代谢物主要富集在蛋白质消化吸收、氨基酸合成、脂质合成等相关通路。通过对不同月龄岗巴绵羊的分析,本研究揭示其血清代谢谱呈现显著差异,L-缬氨酸、L-谷氨酰胺、Bovinic acid等代谢物可能通过参与核苷酸代谢,亚油酸代谢,缬氨酸、亮氨酸及异亮氨酸的生物合成,以及氨酰tRNA的生物合成等关键通路影响岗巴绵羊的生理状况、生长发育等。本研究鉴定到的差异代谢物和代谢通路为进一步明确岗巴绵羊的代谢机制奠定了基础。 展开更多
关键词 岗巴绵羊 差异代谢物 非靶向代谢组学 不同月龄 生长标志代谢物
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A sensitive method of determining optic axis azimuth based on laser feedback 认领 引用 被引量：3
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作者 吴云 张鹏 +1 位作者 陈文学 谈宜东 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第12期272-275,共4页
A sensitive method to determine the optic axis azimuth of the birefringence element is presented, which is based on laser feedback. The phase difference between the two intensities in birefringence feedback changes wi... A sensitive method to determine the optic axis azimuth of the birefringence element is presented, which is based on laser feedback. The phase difference between the two intensities in birefringence feedback changes with the angle between the optic axis of the birefringence element and laser original polarization. The phase difference is highly sensitive to the relative position of the optic axis and the laser original polarization. This method is used to highly precisely determine the optic axis azimuth, and is able to distinguish between the fast axis and the slow axis of the birefringence element. Theoretical analysis and experimental results are both demonstrated. 展开更多
关键词 laser feedback optic axis differential method phase difference
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计算轨道追逃闭环均衡的有限差分方法 认领 引用
20
作者 杨傅云翔 杨乐平 柴华 《国防科技大学学报》 EI CAS CSCD 北大核心 2026年第1期247-261,共15页
针对近距离轨道追逃闭环均衡构造问题,提出一种综合运用Bellman最优性原理、有限差分法和插值技术的计算方法。推导视线坐标系下的博弈系统降维动力学模型,建立近距离轨道追逃博弈模型,降低系统状态空间维度;基于Bellman最优性原理,重... 针对近距离轨道追逃闭环均衡构造问题,提出一种综合运用Bellman最优性原理、有限差分法和插值技术的计算方法。推导视线坐标系下的博弈系统降维动力学模型,建立近距离轨道追逃博弈模型,降低系统状态空间维度;基于Bellman最优性原理,重构原问题为哈密顿-雅可比-艾萨克偏微分方程终值问题,通过逆向分析实现同时处理多组博弈场景;利用Cartesian网格离散状态空间,使用有限差分法计算均衡受动力学驱动的动态演化过程,分析博弈态势;基于控制与均衡空间梯度的关系,使用数值插值构造闭环控制函数;通过数值仿真验证了方法的有效性。 展开更多
关键词 轨道追逃 Bellman最优性原理 有限差分法 微分对策
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