Fourth-order numerical methods for the coupled Korteweg–de Vries equations

Igor Korostil, Simon Clarke

Abstract


We compare six fixed-stepsize fourth-order numerical methods for a number of test problems described by a system of coupled Korteweg–de Vries equations. Particular attention is paid to the ability of these methods to preserve fixed points (solitary waves) and the invariants of the system, and establishing to what extent the conservation of integral invariants is indicative of the solution error for these methods.


doi: 10.1017/S1446181115000012

Keywords


coupled Korteweg–de Vries equations; numerical methods; exponential integrators; implicit Runge–Kutta method



DOI: http://dx.doi.org/10.21914/anziamj.v56i0.8630



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.