A high-order compact scheme for the nonlinear fractional Klein- Gordon equation.

In this article, a high-order finite difference scheme for a kind of nonlinear fractional Klein-Gordon equation is derived. The time fractional derivative is described in the Caputo sense. The solvability of the difference system is discussed by the Leray-Schauder fixed point theorem, while the stability and L∞ convergence of the finite difference scheme are proved by the energy method. Numerical examples are provided to demonstrate the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 706-722, 2015 [ABSTRACT FROM AUTHOR]