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.
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页码：33 / 45
页数：13
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