A high order numerical method for the variable order time-fractional reaction-subdiffusion equation

Abstract

In this paper, we present a high order new numerical approximation for variable order Caputo fractional derivative of order 0<α(x,t)<1, by using the idea of interpolation. Then, by using this approximation, a numerical scheme is presented by using finite difference approach for variable order time fractional reaction-subdiffusion equation (VO-TFRSDE). The unconditionally stability of the numerical scheme is examined theoretically. The scheme is implemented on the two test problems. The numerical results are highly accurate with higher order of convergence. © 2023 The Physical Society of the Republic of China (Taiwan)