A three-level linearized finite difference scheme for the camassa–holm equation



The Camassa–Holm (CH) system is a strong nonlinear third-order evolution equation. So far, the numerical methods for solving this problem are only a few. This article deals with the finite difference solution to the CH equation. A three-level linearized finite difference scheme is derived. The scheme is proved to be conservative, uniquely solvable, and conditionally second-order convergent in both time and space in the discrete L norm. Several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 451–471, 2014