A high order numerical method and its convergence for time-fractional fourth order partial differential equations

Abstract

This paper is concerned with design and analysis of a high order numerical approach based on a uniform mesh to approximate the solution of time-fractional fourth order partial differential equations. In this approach, we first approximate the time-fractional derivative appearing in the governing equation by means of Caputo’s definition and then construct a sextic B-spline collocation method for solving the resulting equation. It is proved that the present method is unconditionally stable. Convergence analysis of the method is discussed. We prove that the method is (2−α)th order convergence with respect to time variable and fourth order convergence with respect to space variable. Three test problems are considered to demonstrate the applicability and efficiency of the new method. It is shown that the rate of convergence predicted theoretically is the same as that obtained experimentally. Numerical results have been compared with those reported previously in literature. It is shown that our method yields more accurate results when compared to the existing methods.