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NUMERICAL SOLUTION OF HYPERBOLIC EQUATIONS AND SYSTEMS WITH TWO INDEPENDENT VARIABLES BY A METHOD OF THE RUNGE-KUTTA TYPEⅠ

机译：用RUNGE-KUTTaⅠ型方法求解具有两个独立变量的双曲型方程组和数值系统

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摘要

Discussed is the application of two-iteration Runge-Kutta algorithms in the solution of the Cauchy problem for hyperbolic equations and systems with two independent variables.

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作者
Nguyen Kong Tuy;
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作者单位

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年度 1968
页码 1-25
总页数 25
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Hyperbolic functions; Iterative solution; Numerical integration; Runge-kutta method; Algorithms; Cauchy problem; Independent variables; Partial differential equations; Translations;

机译：双曲函数;迭代解;数值积分; Runge-kutta方法;算法; Cauchy问题;自变量;偏微分方程;翻译;

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专利

1. Discussion on ????????Numerical solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics????????, ????????Analogue solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics???????? and ????????Analogue solution of elliptic differential equations by conformal transformations???????? [J] . Electrical Engineers, Proceedings of the Institution of . 1971,第6期

机译：用连续特性方法讨论二阶双曲型偏微分方程的数值解??????，二阶双曲型的模拟解偏微分方程的连续特性方法和利用共形变换的椭圆型微分方程的模拟解
2. 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。
3. A Meshless Method for Numerical Solution of a Linear Hyperbolic Equation with Variable Coefficients in Two Space Dimensions [J] . Dehghan M, Shokri A Numerical Methods for Partial Differential Equations: An International Journal . 2009,第2期

机译：二维变系数线性双曲型方程数值解的无网格法。
4. On the parallel implementation and performance study of high-order Rosenbrock-type implicit Runge-Kutta methods for the FR/CPR solutions of the Navier-Stokes equations [C] . Lai Wang, Meilin Yu AIAA aerospace sciences meeting;AIAA SciTech forum . 2018

机译：Navier-Stokes方程FR / CPR解的高阶Rosenbrock型隐式Runge-Kutta方法的并行实现和性能研究
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. Numerical solutions and error estimations for the space fractional diffusion equation with variable coefficients via Fibonacci collocation method [O] . Ayşe Kurt Bahşı, Salih Yalçınbaş -1

机译：斐波那契配点法求解变系数空间分式扩散方程的数值解和误差估计。
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. Numerical solution of hyperbolic equations and systems with two independent variables by a method of the Runge-Kutta type. 1 [R] . Tuy, N. K. 1968

机译：用Runge-Kutta型方法求双曲方程和具有两个自变量的系统的数值解。 1

NUMERICAL SOLUTION OF HYPERBOLIC EQUATIONS AND SYSTEMS WITH TWO INDEPENDENT VARIABLES BY A METHOD OF THE RUNGE-KUTTA TYPEⅠ

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