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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:
65M70Spectral, collocation and related methods (IVP of PDE)
35C10Series solutions of PDE
35L75Nonlinear hyperbolic PDE of higher (>2) order
65M12Stability and convergence of numerical methods (IVP of PDE)
46E22Hilbert spaces with reproducing kernels
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