A Finite-Difference Scheme on a Graded Mesh for Solving Cauchy Problems with a Fractional Caputo Derivative in a Banach Space

被引：0

作者：

Kokurin, M. M. ^{[1
]}

Piskarev, S. I. ^{[1
,2
]}

机构：

[1] Mari State Univ, Yoshkar Ola 424001, Russia

[2] Lomonosov Moscow State Univ, Moscow 119991, Russia

来源：

RUSSIAN MATHEMATICS | 2022年 / 66卷 / 11期

基金：

俄罗斯科学基金会;

关键词：

Cauchy problem; Caputo derivative; Banach space; finite-difference scheme; stability; accuracy estimate; graded mesh; full discretization; INTEGRAL-EQUATIONS; ERROR ANALYSIS; DIFFUSION;

D O I：

10.3103/S1066369X22110044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

study a well-posed Cauchy problem with a fractional Caputo derivative of the order in a Banach space. We construct and explore a finite-difference scheme on a graded mesh a ? (0,1) for solving such problems. The stability and accuracy estimates for a proposed finite-difference scheme are obtained.

引用

页码：33 / 45

页数：13

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