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A finite difference scheme for KdV equation with inhomogeneous boundaries. (Chinese. English summary) Zbl 1488.65234

Summary: We construct a new variable to transform the KdV equation with nonhomogeneous boundaries into the KdV equation with homogeneous boundaries, and propose a three-level second-order accurate linear finite difference scheme for the KdV equation with homogeneous boundaries. The discrete energy method and the von Neumann stability analysis method are used to prove the uniqueness and unconditional stability of the scheme, respectively. Numerical examples are provided to confirm that the scheme is accurate and efficient.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35Q53 KdV equations (Korteweg-de Vries equations)
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