Numerical integration of a coupled Korteweg-de Vries system. (English) Zbl 1035.65095
Summary: We introduce a numerical method for general coupled Korteweg-de Vries systems. The scheme is valid for solving Cauchy problems for an arbitrary number of equations with arbitrary constant coefficients. The numerical scheme takes its legality by proving its stability and convergence, which gives the conditions and the appropriate choice of the grid sizes. The method is applied to the Hirota-Satsuma system and compared with its known explicit solution investigating the influence of initial conditions and grid sizes on accuracy. We also illustrate the method to show the effects of constants with a transition to nonintegrable cases.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
finite difference scheme; numerical examples; Korteweg-de Vries systems; Cauchy problems; stability; convergence; Hirota-Satsuma systemReferences:
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