A meshless numerical solution of the family of generalized fifth-order Korteweg-de Vries equations
arXiv:1008.061951 citationsh-index: 52
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This work provides a numerical technique for solving a specific family of nonlinear partial differential equations, but it is an incremental application of existing methods.
The authors developed a meshless method of lines using radial basis functions and Runge-Kutta integration to solve generalized fifth-order Korteweg-de Vries equations, achieving high accuracy compared to exact solutions.
In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.