On the approximation of solutions of the generalized Korteweg-de Vries-Burger's equation

摘要: Abstract We propose numerical schemes for approximating periodic solutions of the generalized Korteweg—de Vries—Burgers equation. These are based on a Galerkin-finite element formulation spatial discretization and use implicit Runge—Kutta (IRK) methods time stepping. Asymptotically optimal rate convergence estimates can be obtained in terms temporal parameters. In particular, rates classical ones, i.e. no order reduction occurs. also apply Newton's method, to solve system nonlinear equations. Indeed, method yields iterants that converge quadratically preserves convergence.