使用插值缩放函数的分数克莱因-戈登方程谱元法

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Haifa Bin Jebreen
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引用次数: 0

摘要

本文的重点是利用谱元法求分数克莱因-戈登方程的数值解。该算法采用符合特定属性并满足多分辨率分析的插值缩放函数 (ISF)。利用正交投影,该方法可将方程映射到缩放空间。利用表示分数积分和导数算子的矩阵,提出了 ISF 的卡普托分数导数矩阵表示法。利用该矩阵,谱元法可将所需方程还原为代数方程系。为了求解,在该系统的线性和非线性形式中分别使用了广义最小残差法(GMRES 法)和牛顿法。该方法的收敛性已得到证明,一些示例也证实了这一点。该方法的特点是实施简单、效率高、精度高。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Spectral Element Method for Fractional Klein–Gordon Equations Using Interpolating Scaling Functions
The focus of this paper is on utilizing the spectral element method to find the numerical solution of the fractional Klein–Gordon equation. The algorithm employs interpolating scaling functions (ISFs) that meet specific properties and satisfy the multiresolution analysis. Using an orthonormal projection, the equation is mapped to the scaling spaces in this method. A matrix representation of the Caputo fractional derivative of ISFs is presented using matrices representing the fractional integral and derivative operators. Using this matrix, the spectral element method reduces the desired equation to a system of algebraic equations. To find the solution, the generalized minimal residual method (GMRES method) and Newton’s method are used in linear and nonlinear forms of this system, respectively. The method’s convergence is proven, and some illustrative examples confirm it. The method is characterized by its simplicity in implementation, high efficiency, and significant accuracy.
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来源期刊
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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