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An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system. (English) Zbl 1339.65188
Summary: In this paper, we derive an efficient spectral collocation algorithm to solve numerically the nonlinear complex generalized Zakharov system (GZS) subject to initial-boundary conditions. The Jacobi pseudospectral approximation is investigated for spatial approximation of the GZS. It possesses the spectral accuracy in space. The Jacobi-Gauss-Lobatto quadrature rule is established to treat the boundary conditions, and then the problem with its boundary conditions is reduced to a system of ordinary differential equations in time variable. This scheme has the advantage of allowing us to obtain the spectral solution in terms of the Jacobi parameters \(\alpha\) and \(\beta\), which therefore means that the algorithm holds a number of collocation methods as special cases. Finally, two illustrative examples are implemented to assess the efficiency and high accuracy of the Jacobi pseudo-spectral scheme.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
35Q55 NLS equations (nonlinear Schrödinger equations)
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