Avoiding order reduction of Runge-Kutta discretizations for linear time-dependent parabolic problems

DOI10.1023/B:BITN.0000025087.83146.33zbMath1050.65084OpenAlexW1974474574MaRDI QIDQ1826447

Isaías Alonso-Mallo, Begoña Cano

Publication date: 6 August 2004

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/b:bitn.0000025087.83146.33

zbMATH Keywords

convergencemethod of linesinitial boundary value problemsRunge-Kutta methodsorder reductionlinear parabolic problems

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solutions to equations with linear operators (65J10) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Linear differential equations in abstract spaces (34G10)

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Fractional step Runge-Kutta methods for time dependent coefficient parabolic problems ⋮ Analytical and numerical treatment of electro-thermo-mechanical coupling ⋮ Experimental validation of high-order time integration for non-linear heat transfer problems ⋮ Design of DIRK schemes with high weak stage order ⋮ Algebraic Structure of the Weak Stage Order Conditions for Runge–Kutta Methods ⋮ Avoiding order reduction of fractional step Runge-Kutta discretizations for linear time dependent coefficient parabolic problems. ⋮ Optimal time order when implicit Runge-Kutta-Nyström methods solve linear partial differential equations ⋮ Simulating the temporal change of the active response of arteries by finite elements with high-order time-integrators ⋮ New low order Runge-Kutta schemes for asymptotically exact global error estimation of embedded methods without order reduction ⋮ Implicit Taylor methods for parabolic problems with nonsmooth data and applications to optimal heat control

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