A Linearised Three-Point Combined Compact Difference Method with Weighted Approximation for Nonlinear Time Fractional Klein-Gordon Equations

Abstract

A numerical method for nonlinear time fractional Klein-Gordon equations is studied. Discretising spatial and temporal variables by a combined compact difference and a weighted approximation, respectively, we develop a linearised method for the equations under consideration. It has at least sixth-order accuracy in space and second-order accuracy in time. Numerical examples demonstrate the effectiveness and accuracy of the method.