A numerical method for solving the nonlinear fermi–pasta–ulam problem

An effective finite difference scheme for solving the nonlinear Fermi–Pasta–Ulam (FPU) problem is derived. The most important feature of the scheme inherits energy conservation property from the nonlinear FPU problem. The unique solvability and the convergence of the difference scheme are proved by the energy method. The convergence order is in the maximum norm, where τ is the temporal grid size and h is the spatial grid size, respectively. In addition, the stability of the difference scheme is obtained. Numerical results are presented to support the theoretical analysis and verify numerically the energy conservation property.© 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 187‐209, 2014