A comparison between numerical solutions to fractional differential equations: Adams-type predictor-corrector and multi-step generalized differential transform method

TL;DR

This paper compares two numerical methods for solving fractional differential equations, highlighting that the multi-step generalized differential transform method lacks accuracy over large domains due to neglecting non-local effects.

Contribution

It provides a comparative analysis of Adams-type predictor-corrector and MSGDTM methods, revealing limitations of MSGDTM in handling non-local fractional derivatives.

Findings

MSGDTM neglects non-local effects of fractional derivatives.

MSGDTM is less accurate over large domains.

Adams-Bashforth-Moulton method performs better for FDEs.

Abstract

In this note, two numerical methods of solving fractional differential equations (FDEs) are briefly described, namely predictor-corrector approach of Adams-Bashforth-Moulton type and multi-step generalized differential transform method (MSGDTM), and then a demonstrating example is given to compare the results of the methods. It is shown that the MSGDTM, which is an enhancement of the generalized differential transform method, neglects the effect of non-local structure of fractional differentiation operators and fails to accurately solve the FDEs over large domains.