Afrika Matematika

, Volume 29, Issue 7–8, pp 1203–1214

# An efficient meshless method based on RBFs for the time fractional diffusion-wave equation

• Elyas Shivanian
Article

## Abstract

This paper proposes a numerical method to deal with time-fractional diffusion-wave equation (one-dimensional and two-dimensional). The time-fractional term of the problem is scheduled in Caputo sense which is popular in analyzing time-fractional dependent problems. The proposed technique is based on radial basis functions and more, it is a kind of meshless method, therefore it is not difficult applying the method to handle two or three dimensional time-fractional diffusion-wave problems especially when the domain are more general and not regular forms. The generalized thin plate splines (GTPS) radial basis functions are employed. Numerical examples are given to test the accuracy. Three numerical experiments reveal that proposed method is very convenient for solving such problems.

## Keywords

Radial basis function Fractional PDE Diffusion-wave equation Kansa’s method Finite differences $$\theta$$-method

## Mathematics Subject Classifcation

65M06 65N12 26A33

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© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018