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Orthogonal cubic spline collocation method for the extended Fisher–Kolmogorov equation. (English) Zbl 1067.65107

The extended Fisher-Kolmogorov equation, first transformed into a system of second order equations, is discretized in space using a collocation method with orthogonal cubic splines. The resulting semidiscrete system leads to nonlinear differential algebraic equations of index one. A priori bounds are derived which guarantee the global existence of a unique solution. Finally, numerical experiments are presented which confirm the theoretical 4th-order convergence of the scheme. Time integration is performed with a three stage implicit Runge-Kutta scheme of 5th-order.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
62M20 Inference from stochastic processes and prediction
35Q35 PDEs in connection with fluid mechanics
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L80 Numerical methods for differential-algebraic equations
34A09 Implicit ordinary differential equations, differential-algebraic equations

Software:

RODAS; ABDPACK
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References:

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