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Partitioned Runge-Kutta methods for partial differential equations (The Numerical Solution of Differential Equations and Linear Computation)

机译：偏微分方程的分区Runge-Kutta方法（微分方程和线性计算的数值解）

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Koto Toshiyuki;
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年度 2003
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1. In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given. [J] . M. M. Khader, M. Adel Nonlinear engineering: Modeling and application . 2016,第3期

机译：在本文中，我们采用分数阶复杂变换方法将非线性分数阶Klein-Gordon方程（FKGE）转换为常微分方程。我们使用变分迭代方法（VIM）来解决所得的ODE。分数导数以Caputo形式表示。提出了一些数值例子来验证所提出的技术。最后，与使用四阶Runge-Kutta的数值解进行了比较。
2. A Numerical Computation of a System of Linear and Nonlinear Time Dependent Partial Differential Equations Using Reduced Differential Transform Method [J] . Brajesh Kumar Singh, Mahendra International Journal of Differential Equations . 2016,第Null期

机译：线性和非线性时变偏微分方程组的简化微分变换法数值计算
3. Fractional reduced differential transform method for numerical computation of a system of linear and nonlinear fractional partial differential equations [J] . Brajesh Kumar Singh International Journal of Open Problems in Computer Science and Mathematics . 2016,第3期

机译：用于线性和非线性分数阶偏微分方程组数值计算的分数阶简化微分变换方法
4. The Jacobin elliptic function expansion method for solitonic solutions to nonlinear partial differential equations with symbolic computation [C] . Zhao Xiqiang, Sun Weijun 2011 Seventh International Conference on Natural Computation . 2011

机译：带有符号计算的非线性偏微分方程孤子解的雅可比椭圆函数展开法
5. Numerical solution of retarded and neutral delay differential equations using continuous Runge-Kutta methods. [D] . Hayashi, Hiroshi. 1996

机译：使用连续Runge-Kutta方法的延迟和中立延迟微分方程的数值解。
6. A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things [O] . Rohul Amin, Shah Nazir, Iván García-Magariño 2020

机译：无线传感器网络与物联网非线性时滞积分微分方程数值解的配置方法
7. A Runge-Kutta Method for the Numerical Solution of the Goursat Problem in Hyperbolic Partial Differential Equations [O] . J. T. Day 1966

机译：双曲线偏微分方程中Goursat问题数值解的runge-kutta方法
8. New Methods for Numerical Solution of One Class of Strongly Nonlinear Partial Differential Equations with Applications [R] . Oliker, V. I., Waltman, P. 1987

机译：一类强非线性偏微分方程数值解的新方法及其应用

Partitioned Runge-Kutta methods for partial differential equations (The Numerical Solution of Differential Equations and Linear Computation)

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