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Hai, Doan Duy; Yagi, Atsushi

Rosenbrock strong stability-preserving methods for convection-diffusion-reaction equations. (English) Zbl 1297.65082

Japan J. Ind. Appl. Math. 31, No. 2, 401-417 (2014).
Summary: Rosenbrock methods are normally used for solving moderately stiff problems and strong-stability preserving ones are employed a lot for hyperbolic conservation laws. Their combination called additive Rosenbrock-strong stability preserving (Ros-SSP) schemes are first introduced in this paper to deal with convection-diffusion-reaction equations. Accuracy and stability of the Ros-SSP scheme are considered. Numerical results are given to prove advantages of Ros-SSP methods. A practical application of a three-stage, second order Ros-SSP method solving a spatially discretized angiogenesis model in two-dimensional case is provided as well.

Cited in 3 Documents

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L05 Numerical methods for initial value problems involving ordinary differential equations
35L57 Initial-boundary value problems for higher-order hyperbolic systems
65L20 Stability and convergence of numerical methods for ordinary differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
92C17 Cell movement (chemotaxis, etc.)

Keywords:

Runge-Kutta methods; Rosenbrock methods; convection-diffusion-reaction equations; strong stability-preserving; time discretization; stiff problems; hyperbolic conservation laws; numerical result; angiogenesis model
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References:

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