Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping

The purpose of the current investigation is to determine numerical solution of time-fractional diffusion-wave equation with damping for Caputo's fractional derivative of order α  (1<α≤2)(1<α≤2). A meshless local radial point interpolation (MLRPI) scheme based on Galerkin weak form is analyzed. The reason of choosing MLRPI approach is that it does not require any background integrations cells, instead integrations are implemented over local quadrature domains which are further simplified for reducing the complication of computation using regular and simple shape. The unconditional stability and convergence with order O(τ6−2α)O(τ6−2α) are proved, where τ is time stepping. Also, several numerical experiments are illustrated to verify theoretical analysis.