Discrete Singular Convolution Method for Numerical Solutions of Fifth Order Korteweg-De Vries Equations

DOI: 10.4236/jamp.2013.17002   PDF   HTML   XML   3,802 Downloads   6,623 Views   Citations


A new computational method for solving the fifth order Korteweg-de Vries (fKdV) equation is proposed. The nonlinear partial differential equation is discretized in space using the discrete singular convolution (DSC) scheme and an exponential time integration scheme combined with the best rational approximations based on the Carathéodory-Fejér procedure for time discretization. We check several numerical results of our approach against available analytical solutions. In addition, we computed the conservation laws of the fKdV equation. We find that the DSC approach is a very accurate, efficient and reliable method for solving nonlinear partial differential equations.

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Pindza, E. and Maré, E. (2013) Discrete Singular Convolution Method for Numerical Solutions of Fifth Order Korteweg-De Vries Equations. Journal of Applied Mathematics and Physics, 1, 5-15. doi: 10.4236/jamp.2013.17002.

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The authors declare no conflicts of interest.


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