A semi-analytical collocation method for solving multi-term variable-order time fractional partial differential equations

TL;DR

This paper introduces a semi-analytical collocation method combining Fourier series and backward substitution to efficiently solve complex multi-term variable-order time fractional PDEs, verified by numerical examples.

Contribution

It develops a novel semi-analytical approach that transforms multi-term VOTFPDEs into solvable VOTFODEs, enhancing accuracy and efficiency.

Findings

Method accurately solves multi-term VOTFPDEs

Numerical examples confirm high efficiency

Approach outperforms existing methods

Abstract

This paper presents a novel semi-analytical collocation method to solve multi-term variable-order time fractional partial differential equations (VOTFPDEs). In the proposed method it employs the Fourier series expansion for spatial discretization, which transforms the original multi-term VOTFPDEs into a sequence of multi-term variable-order time fractional ordinary differential equations (VOTFODEs). Then these VOTFODEs can be solved by using the recent-developed backward substitution method. Several numerical examples verify the accuracy and efficiency of the proposed numerical approach in the solution of multi-term VOTFPDEs.