Adaptive meshless numerical method of solving 2D variable order time fractional mobile-immobile advection-diffusion equations

Abstract

This paper inspires us to propose an adaptive meshless numerical method of solving a 2D variable order time fractional mobile-immobile advection-diffusion equation on arbitrary domain. The mentioned method has three main contributions. (i) The adaptive meshless method could decrease amounts of computations effectively. (ii) On arbitrary domain, we successfully apply Legendre multiwaves in reproducing kernel Hilbert space (RKHS) defined on rectangle domain to approximate the exact solution. (iii) We skillfully build a special spline space, convergence order is obtained in view of convergence theories of spline space. Numerical experiments further demonstrate the validity of the method. • The adaptive meshless method could decrease amounts of computations effectively. • On arbitrary domain, we apply Legendre multiwaves to approximate the exact solution using some approximation theorems. • We successfully give the error estimate in the case of low regularity of the function.