A Fully Galerkin Method for the Damped Generalized Regularized Long-Wave (DGRLW) Equation

摘要

In this article, a fully discrete Galerkin scheme based on a nonlinear Crank-Nicolson method to approximate the solution of the DGRLW equation is constructed. Some a priori bounds are proved as well as error estimates. Then, a linearized modification scheme by an extrapolation method is discussed. The two schemes are time second order convergence. The last part is devoted to some numerical results.