A linearized second-order scheme for nonlinear time fractional Klein-Gordon type equations
It provides a rigorous convergence analysis for a numerical method solving a class of nonlinear fractional PDEs, which is incremental for computational mathematics.
The paper proposes a linearized difference scheme for nonlinear time fractional Klein-Gordon equations, avoiding iterative methods, and proves second-order convergence in time.
We consider difference schemes for nonlinear time fractional Klein-Gordon type equations in this paper. A linearized scheme is proposed to solve the problem. As a result, iterative method need not be employed. One of the main difficulties for the analysis is that certain weight averages of the approximated solutions are considered in the discretization and standard energy estimates cannot be applied directly. By introducing a new grid function, which further approximates the solution, and using ideas in some recent studies, we show that the method converges with second-order accuracy in time.