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Solving the generalized regularized long wave equation on the basis of a reproducing kernel space. (English) Zbl 1220.65143

On the basis of a reproducing kernel space, an iterative algorithm for solving the generalized regularized long wave equation is presented. The analytical solution in the reproducing kernel space is shown in a series form and the approximate solution \(u_{n}\) is constructed by truncating the series to \(n\) terms. The convergence of \(u_{n}\) to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such evolution equations

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35C10 Series solutions to PDEs
35L75 Higher-order nonlinear hyperbolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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