利用赫米特插值法实现时空里兹-卡普托变阶分数波方程的显式有限差分近似法

IF 0.4 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications Pub Date : 2024-09-13 DOI:10.1134/s1995423924030054

Chol Won O, Won Myong Ro, Yun Chol Kim

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引用次数: 0

摘要

摘要变阶分数算子可用于各种物理和生物应用中，其中相关量的变化率可能取决于空间和/或时间。在本文中，我们提出了一种显式有限差分近似方法，用于有限域中具有初始条件和边界条件的时空 Riesz-Caputo 变阶分数波方程。所提出的方案具有条件稳定性和全局截断误差 \(O(\tau^{2}+h^{2})\)。我们还通过数值实验验证了所提方案的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

An Explicit Finite Difference Approximation for Space-Time Riesz–Caputo Variable Order Fractional Wave Equation Using Hermitian Interpolation

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An Explicit Finite Difference Approximation for Space-Time Riesz–Caputo Variable Order Fractional Wave Equation Using Hermitian Interpolation

Abstract

Variable order fractional operators can be used in various physical and biological applications where rates of change of the quantity of interest may depend on space and/or time. In this paper, we propose an explicit finite difference approximation for space-time Riesz–Caputo variable order fractional wave equation with initial and boundary conditions in a finite domain. The proposed scheme is conditionally stable and has global truncation error \(O(\tau^{2}+h^{2})\). We also present a numerical experiment to verify the efficiency of the proposed scheme.

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来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.