Analysis of the Time Fractional 2-D Diffusion-Wave Equation via Moving Least Square (MLS) Approximation

Abstract

In this paper, the time fractional two-dimensional diffusion-wave equation defined by Caputo sense for ( $$1<\alpha <2$$ ) is analyzed by an efficient and accurate computational method namely meshless local Petrov–Galerkin (MLPG) method which is based on the Galerkin weak form and moving least squares (MLS) approximation. We consider a general domain with Dirichlet boundary conditions further to given initial values as continuous functions. Meshless Galerkin weak form is adopted to the interior nodes while the meshless collocation technique is applied for the nodes on the boundaries of the domain. Since Dirichlet boundary condition is imposed directly therefore the general domains are also applicable easily. In MLPG method, the MLS approximation is usually used to construct shape functions which plays important rule in the convergence and stability of the method. It is proved the method is unconditionally stable in some sense. Two numerical examples are presented, one of them with the regular domain and the other one with non-regular domain, and satisfactory agreements are achieved.