A novel finite difference technique with error estimate for time fractional partial integro-differential equation of Volterra type

被引：40
作者：
Santra, S. [1 ]
Mohapatra, J. [1 ]
机构：
[1] Natl Inst Technol Rourkela, Dept Math, Rourkela, Odisha, India
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 400卷
关键词：
Partial integro-differential equation; Caputo fractional derivative; L1; scheme; Error analysis; NUMERICAL-METHOD; INTEGRAL-EQUATIONS; BERNOULLI WAVELETS; DOMAINS; ORDER;
D O I：
10.1016/j.cam.2021.113746
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main purpose of this work is to study the numerical solution of a time fractional partial integro-differential equation of Volterra type, where the time derivative is defined in Caputo sense. Our method is a combination of the classical L1 scheme for temporal derivative, the general second order central difference approximation for spatial derivative and the repeated quadrature rule for integral part. The error analysis is carried out and it is shown that the approximate solution converges to the exact solution. Several examples are given in support of the theoretical findings. In addition, we have shown that the order of convergence is more high on any subdomain away from the origin compared to the entire domain. (C) 2021 Elsevier B.V. All rights reserved.
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页数：13
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