Efficient linearly implicit methods for nonlinear multidimensional parabolic problems.

DOI10.1016/j.cam.2003.11.008zbMath1038.65087OpenAlexW2074316966MaRDI QIDQ1426765

J. C. Jorge, B. Bujanda

Publication date: 15 March 2004

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.2003.11.008

zbMATH Keywords

AlgorithmsConvergenceStabilityADI methodsNumerical examplesSemidiscretizationNonlinear parabolic problemsAdditive Runge-Kutta methodStiff nonlinear initial value problems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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)

Related Items (5)

A unified formulation of splitting-based implicit time integration schemes ⋮ Arbitrary high-order unconditionally stable methods for reaction-diffusion equations with inhomogeneous boundary condition via deferred correction ⋮ A new class of second order linearly implicit fractional step methods ⋮ Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems ⋮ Stability results for linearly implicit fractional step discretizations of nonlinear time dependent parabolic problems

Cites Work

• A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems
• Additive Runge-Kutta methods for the resolution of linear parabolic problems
• 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
• Approximative methods for nonlinear equations (two approaches to the convergence problem)
• An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems
• Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations
• Stability results for fractional step discretizations of time dependent coefficient evolutionary problems
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