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A novel method for solving KdV equation based on reproducing kernel Hilbert space method. (English) Zbl 1266.65178

Summary: We propose a reproducing kernel method for solving the Korteweg-de Vries (KdV) equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples are also studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
35Q53 KdV equations (Korteweg-de Vries equations)
35C10 Series solutions to PDEs
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References:

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