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A variable time-step-size code for advection-diffusion-reaction PDEs. (English) Zbl 1259.65137

An adaptive method for the time integration of initial value problems in ordinary differential equations resulting from the spatial discretization of 2D or 3D PDEs of advection-diffusion-reaction type is developed. The spatial discretization is made by means of finite difference schemes and the time integration relies on the two stage Radau IIA method. Some stability results and a local error estimate are derived. The method is applied to four standard problems and the scheme is compared with already existing solvers.

MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs

Software:

RODAS; LSODA; RKC; IRKC
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Full Text: DOI

References:

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