MLPG method based on particular solution to identify a time-dependent boundary source for the time-fractional diffusion equation

Abstract

This paper presents a meshless local Petrov–Galerkin method based on the particular solution (MLPG-PS) to solve a time-fractional inverse problem with unknown boundary condition. The particular solution obtained by using multiquadric radial basis function is used to construct basis function. First, we apply a finite difference method to discretize time-fractional derivative. Then, we use MLPG-PS method to approximate the spatial derivative. Since the coefficient matrix is ill-conditioned, the Tikhonov regularization technique is employed to solve the resulting system. Two numerical examples are tested to show the accuracy and efficiency of the proposed method.

Keywords:

• Time-fractional diffusion equation
• MLPG method
• particular solution

2010 Mathematics Subject Classifications:

• 65-XX
• 65MXX
• 65M32

Acknowledgments

The author is very grateful to anonymous reviewers for carefully reading the paper and for their valuable comments and suggestions which have improved the paper very much.

Disclosure statement

No potential conflict of interest was reported by the author.