A new class of second order linearly implicit fractional step methods

DOI10.1016/j.cam.2008.01.016zbMath1143.65074OpenAlexW1987620918MaRDI QIDQ932748

J. C. Jorge, Laura Portero

Publication date: 11 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.cam.2008.01.016

zbMATH Keywords

stabilityconvergencesemilinear parabolic problemsdomain decompositionerror boundsRunge-Kutta methodsemidiscretizationfractional step methods

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items (5)

Reprint of ``Domain decomposition multigrid methods for nonlinear reaction-diffusion problems ⋮ Domain decomposition operator splitting for mimetic finite difference discretizations of non-stationary problems ⋮ Locally linearized fractional step methods for nonlinear parabolic problems ⋮ Convergence of fractional step mimetic finite difference discretizations for semilinear parabolic problems ⋮ Domain decomposition multigrid methods for nonlinear reaction-diffusion problems

Uses Software

• KELLEY

Cites Work

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• A generalization of Peaceman-Rachford fractional step method.
• Efficient linearly implicit methods for nonlinear multidimensional parabolic problems.
• Additive Runge-Kutta schemes for convection-diffusion-reaction equations
• Stability results for linearly implicit fractional step discretizations of nonlinear time dependent parabolic problems
• Positive Steady-state Solutions of a Non-linear Reaction-Diffusion System
• Order conditions for linearly implicit fractional step Runge Kutta methods
• A Nonlinear Alternating Direction Method
• Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations

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