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Numerical solution of nonlinear Jaulent-Miodek and Whitham-Broer-Kaup equations. (English) Zbl 1266.65176
Summary: We investigate the numerical solution of Jaulent-Miodek (JM) and Whitham-Broer-Kaup (WBK) equations. The proposed numerical schemes are based on the fourth-order time-stepping schemes in combination with discrete Fourier transform. We discretize the original partial differential equations with discrete Fourier transform in space and obtain a system of ordinary differential equations (ODEs) in Fourier space which are solved with fourth-order time-stepping methods. After transforming the equations to a system of ODEs, the linear operator in the JM equation is diagonal, but in the WBK equation it is not diagonal. However, for the WBK equation we can also implement the methods such as diagonal case which reduces the CPU time. Comparing numerical solutions with analytical solutions demonstrate that those methods are accurate and readily implemented.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics
65T50 Numerical methods for discrete and fast Fourier transforms
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
Software:
Matlab
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