An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system

• Published in: Applied mathematics and computation Vol. 247; pp. 30 - 46
• Main Author: Bhrawy, A.H.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.11.2014
• Subjects: Accuracy; Algorithms; Approximation; Boundary conditions; Jacobi–Gauss–Lobatto quadrature; Mathematical analysis; Mathematical models; Nonlinear complex Zakharov-types equations; Nonlinearity; Pseudo-spectral scheme; Spectra; Two-stage implicit Runge–Kutta; Nonlinear complex Zakharov-types equations; Pseudo-spectral scheme; Two-stage implicit Runge–Kutta; Jacobi–Gauss–Lobatto quadrature
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2014.08.062

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 α and β, 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.