A comparison between numerical solutions to fractional differential equations: Adams-type predictor-corrector and multi-step generalized differential transform method
For researchers using numerical methods for fractional differential equations, this paper provides a cautionary comparison showing limitations of MSGDTM.
The paper compares two numerical methods for solving fractional differential equations and finds that the multi-step generalized differential transform method fails to accurately solve FDEs over large domains due to neglecting non-local structure.
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.