Numerical solution of nonlinear Jaulent-Miodek and Whitham-Broer-Kaup equations

作者：Mohebbi Akbar^*; Asgari Zohreh; Dehghan Mehdi

来源：Communications in Nonlinear Science & Numerical Simulation, 2012, 17(12): 4602-4610.

DOI：10.1016/j.cnsns.2012.04.011

• Jaulent-Miodek equation
• Whitham-Broer-Kaup equation
• Exponential time differencing
• Integrating factor
• Spectral methods
• High accuracy

In this work 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 (PDEs) with discrete Fourier transform in space and obtain a system of ordinary differential equations (ODEs) in Fourier space which will be solved with fourth order time-stepping methods. After transforming the equations to a system of ODEs, the linear operator in JM equation is diagonal but in WBK equation is not diagonal. However for WBK equation we can also implement the methods such as diagonal case which reduces the CPU time. Comparing numerical solutions with analytical solutions demonstrates that those methods are accurate and readily implemented.

• 出版日期2012-12