双曲电报方程的新解

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Mohammad Partohaghighi, M. Akinlar, G. Weber
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引用次数: 3

摘要

提出了一种基于虚拟时间积分(FTI)和群保持(GP)方法统一的新方法。将FTI方法应用于给定偏微分方程得到的数值离散常微分方程,并将GP方法应用于数值离散常微分方程。该算法应用于双曲电报方程,利用了Cayley变换和Minkowski空间中的Pade近似。它避免了非真实解和鬼不动点,这是本方法相对于文献中其他相关数值方法的优点之一。通过三个具体实例对电报方程和离散步骤中出现的各种参数值进行了测试。本文首次得到了这类电报方程的解。提供了说明数字。通过对数值解与精确解进行误差分析,确定了该方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
New solutions of hyperbolic telegraph equation
We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation (PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points which is one of the advantages of the present method over other related numerical methods in the literature. The technique is tested on three specific examples for various parameter values appearing in the telegraph equation and discretization steps. Such solutions of the telegraph equation are obtained first time in this paper. Illustrative figures are provided. Efficiency of the method is determined by an error analysis which is achieved by comparing numerical solutions with exact solutions.
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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