Higher order graded mesh scheme for time fractional differential equations

In this article, we propose a higher order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, in order to obtain the approximate solution of time fractional partial differential equations (TFPDE). The proposed ap...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-01
Main Authors: Gande Naga Raju, Madduri, Harshita
Format: Article
Language:English
Subjects:
Approximation
Error analysis
Mathematical analysis
Partial differential equations
Stability analysis
Truncation errors
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we propose a higher order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, in order to obtain the approximate solution of time fractional partial differential equations (TFPDE). The proposed approximation for C-F derivative tackles the singularity at origin effectively and is easily applicable to diverse problems. The stability analysis and truncation error bounds of the proposed scheme are discussed, along with this, analyzed the required regularity of the solution. Few numerical examples are presented to support the theory.
ISSN:2331-8422