A simple adaptive technique for nonlinear wave problems
Journal of Computational Physics
Symbolic methods to construct exact solutions of nonlinear partial differential equations
Mathematics and Computers in Simulation - Special issue: computation of nonlinear phenomena
Padé numerical method for the Rosenau-Hyman compacton equation
Mathematics and Computers in Simulation
Self-similar radiation from numerical Rosenau-Hyman compactons
Journal of Computational Physics
Journal of Computational and Applied Mathematics
ACM Transactions on Mathematical Software (TOMS)
Radiation in numerical compactons from finite element methods
MATH'05 Proceedings of the 8th WSEAS International Conference on Applied Mathematics
Computers & Mathematics with Applications
Different physical structures of solutions for a generalized Boussinesq wave equation
Journal of Computational and Applied Mathematics
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In this study, we consider partial differential equation problems describing nonlinear wave phenomena, e.g., a fully nonlinear third order Korteweg-de Vries (KdV) equation, the fourth order Boussinesq equation, the fifth order Kaup-Kupershmidt equation and an extended KdV5 equation. First, we develop a method of lines solution strategy, using an adaptive mesh refinement algorithm based on the equidistribution principle and spatial regularization techniques. On the resulting highly nonuniform spatial grids, the computation of high-order derivative terms appears particularly delicate and we focus attention on the selection of appropriate approximation techniques. Finally, we solve several illustrative problems and compare our computational approach to conventional solution techniques.