{"title":"An Explicit Finite Difference Approximation for Space-Time Riesz–Caputo Variable Order Fractional Wave Equation Using Hermitian Interpolation","authors":"Chol Won O, Won Myong Ro, Yun Chol Kim","doi":"10.1134/s1995423924030054","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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 <span>\\(O(\\tau^{2}+h^{2})\\)</span>. We also present a numerical experiment to verify the efficiency of the proposed scheme.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"206 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995423924030054","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
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.
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.
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