Analysis of a meshless method for the time fractional diffusion-wave equation

چکیده مقاله

Abstract In this paper a numerical technique is proposed for solving the time frac- tional diffusion-wave equation. We obtain a time discrete scheme based on finite difference formula. Then, we prove that the time discrete scheme is unconditionally stable and convergent using the energy method and the convergence order of the time discrete scheme is O(τ 3 −α ). Firstly, we change the main problem based on Dirich- let boundary condition to a new problem based on Robin boundary condition and then, we consider a semi-discrete scheme with Robin boundary condition and show when β →+∞ solution of the main semi-discrete problem with Dirichlet bound- ary condition is convergent to the solution of the new semi-discrete problem with Robin boundary condition. We consider the new semi-discrete problem with Robin boundary condition and use the meshless Galerkin method to approximate the spatial derivatives. Finally, we obtain an error bound for the new problem. We prove that con- vergence order of the numerical scheme based on Galekin meshless is O(h).Inthe considered method the appeared integrals are approximated using Gauss Legendre quadrature formula. The main aim of the current paper is to obtain an error estimate