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Discrete singular convolution for the generalized variable-coefficient Korteweg-de Vries equation. (English) Zbl 1450.65082

Summary: Numerical solutions of the generalized variable-coefficient Korteweg-de Vries equation are obtained using a discrete singular convolution and a fourth order singly diagonally implicit Runge-Kutta method for space and time discretisation, respectively. The theoretical convergence of the proposed method is rigorously investigated. Test problems including propagation of single solitons and interaction of solitary waves are performed to verify the efficiency and accuracy of the method. The numerical results are checked against available analytical solutions and compared with the Sinc numerical method. We find that our approach is a very accurate, efficient and reliable method for solving nonlinear partial differential equations.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics

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