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Stability analysis of a high-order finite-difference scheme for the Korteweg-de Vries equation with non-homogeneous boundaries. (English) Zbl 1476.65211

Summary: In this paper, we analyze the stability of a high-order finite-difference scheme for the Korteweg-de Vries (KdV) equation with non-homogeneous boundaries. We first employ a variable transformation to change the non-homogeneous boundaries to homogeneous boundaries. We then develop a fourth-order accurate finite-difference scheme for solving the transformed KdV problem. The stability, convergence and solvability of the numerical solution are analyzed. Numerical examples are given to confirm the good accuracy and the effectiveness of the present method for handling the KdV equations with non-homogeneous boundaries.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
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