Two‐level linearized and local uncoupled difference schemes for the two‐component evolutionary Korteweg‐de Vries system

Abstract

AbstractThe two‐level linearized and local uncoupled spatial second order and compact difference schemes are derived for the two‐component evolutionary system of nonhomogeneous Korteweg‐de Vries equations. It is shown by the mathematical induction that these two schemes are uniquely solvable and convergent in a discrete L∞ norm with the convergence order of O(τ2 + h2) and O(τ2 + h4), respectively, where τ and h are the step sizes in time and space. Three numerical examples are given to confirm the theoretical results.