A Lagrange-quadratic spline optimal collocation method for the time tempered fractional diffusion equation

Abstract

In the current paper, for the time fractional diffusion equation with an exponential tempering, we propose a numerical algorithm based on the Lagrange-quadratic spline interpolations and the optimal technique. The discretized linear systems and some properties are investigated in detail. By using these properties, the coefficient matrix and the right-hand term at each time step are given to analyze the computational cost. Theoretical analyses show that this proposed method enjoys both stability and convergence order of O(τ2+h4). Some numerical examples are provided to verify the practical feasibility and efficiency of the proposed scheme.