A Robust Collocation Method for Time Fractional PDEs Based on Mean Value Theorem and Cubic B-Splines

This paper explains and applies a numerical technique utilizing the cubic B-spline functions and the mean value theorem (MVT) to solve a general time fractional partial differential equation (FPDE). The MVT for integrals enables us to approximate the time fractional derivatives in an appropriate simple form. We use the cubic B-spline functions to construct the numerical solution and its spatial derivatives. The great advantage of our technique is that it enables us to approximate solutions of many time FPDEs for several choices of F(x, t, u, ux, uxx). Two numerical examples have been included to emphasize the accuracy and efficiency of the method. It is demonstrated that the numerical method is unconditionally stable by employing the Von Neumann method (VNM).