Partitioned Runge–Kutta–Chebyshev Methods for Diffusion-Advection-Reaction Problems

DOI10.1137/100807892zbMath1245.65120OpenAlexW1986785137MaRDI QIDQ3103538

C. J. Zbinden

Publication date: 7 December 2011

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/100807892

zbMATH Keywords

stabilitynumerical examplesstiff equationssemidiscretizationadvection-diffusion equationpartitioned Runge-Kutta methodsparabolic integro-differential equationRunge-Kutta-Chebyshev methodsBrusselator problem

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for stiff equations (65L04)

Related Items (9)

When and how to split? A comparison of two IMEX splitting techniques for solving advection-diffusion-reaction equations ⋮ Explicit stabilised gradient descent for faster strongly convex optimisation ⋮ PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise ⋮ Explicit stabilized multirate method for stiff differential equations ⋮ Conservative stabilized Runge-Kutta methods for the Vlasov-Fokker-Planck equation ⋮ A fully adaptive explicit stabilized integrator for advection-diffusion-reaction problems ⋮ Spectral properties and conservation laws in mimetic finite difference methods for PDEs ⋮ Towards optimal explicit time-stepping schemes for the gyrokinetic equations ⋮ Explicit Stabilized Integrators for Stiff Optimal Control Problems

Uses Software

• IRKC
• RKC
• S-ROCK

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