A linearized second-order scheme for nonlinear time fractional Klein-Gordon type equations

摘要

We consider difference schemes for nonlinear time fractional Klein-Gordontype equations in this paper. A linearized scheme is proposed to solve theproblem. As a result, iterative method need not be employed. One of the maindifficulties for the analysis is that certain weight averages of theapproximated solutions are considered in the discretization and standard energyestimates cannot be applied directly. By introducing a new grid function, whichfurther approximates the solution, and using ideas in some recent studies, weshow that the method converges with second-order accuracy in time.