Additive Runge-Kutta methods for the resolution of linear parabolic problems

DOI10.1016/S0377-0427(01)00475-7zbMath1007.65047MaRDI QIDQ1602768

J. C. Jorge, B. Bujanda

Publication date: 24 June 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

consistencyA-stabilityadditive Runge-Kutta methodevolutionary convection-diffusion problem

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (7)

Fractional step Runge-Kutta methods for time dependent coefficient parabolic problems ⋮ A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations ⋮ Variable step-size fractional step Runge-Kutta methods for time-dependent partial differential equations ⋮ Efficient linearly implicit methods for nonlinear multidimensional parabolic problems. ⋮ Numerical methods for evolutionary reaction-diffusion problems with nonlinear reaction terms. ⋮ Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems ⋮ Domain decomposition operator splitting for mimetic finite difference discretizations of non-stationary problems

Cites Work

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• A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems
• Contractivity results for alternating direction schemes in Hilbert spaces
• The development of Runge-Kutta methods for partial differential equations
• Additive Runge-Kutta Methods for Stiff Ordinary Differential Equations
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Additive Methods for the Numerical Solution of Ordinary Differential Equations
• Trapezoidal and midpoint splittings for initial-boundary value problems
• Stability results for fractional step discretizations of time dependent coefficient evolutionary problems

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