An extension ofA-stability to alternating direction implicit methods

DOI10.1007/BF01930993zbMath0448.65058MaRDI QIDQ3894915

Robert F. Warming, Richard M. Beam

Publication date: 1979

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

A-stabilityalternating direction implicit methodsmethod of approximate factorizationA- stable linear multistep methodcompletely implicit, noniterative, finite-difference schemesmixed hyperbolic-parabolic partial differential equations

Mathematics Subject Classification ID

Heat equation (35K05) 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) Iterative numerical methods for linear systems (65F10) Initial value problems for second-order parabolic equations (35K15) Initial value problems for second-order hyperbolic equations (35L15) Partial differential equations of mixed type and mixed-type systems of partial differential equations (35M99)

Related Items (16)

Splitting methods for fourth order parabolic partial differential equations ⋮ Parallel solution of a coupled flow and transport model for shallow water ⋮ High order difference methods for heat equation in polar cylindrical coordinates ⋮ Reflections on the evolution of implicit Navier-Stokes algorithms ⋮ Approximate factorization for a viscous wave equation ⋮ On the Quasi-unconditional Stability of BDF-ADI Solvers for the Compressible Navier--Stokes Equations and Related Linear Problems ⋮ On variable step highly stable 4-stage Hermite-Birkhoff solvers for stiff ODEs ⋮ A note on stability of the Douglas splitting method ⋮ Semi-implicit Runge-Kutta schemes for the Navier-Stokes equations ⋮ A comparison of integration methods for atmospheric transport-chemistry problems ⋮ Approximate factorization for time-dependent partial differential equations ⋮ Iterative and noniterative, full and approximate factorization methods for multidimensional reaction-diffusion equations ⋮ An overview and generalization of implicit Navier-Stokes algorithms and approximate factoriza\-tion. ⋮ A comparison of some codes for the stiff oscillatory problem ⋮ Improved accuracy for the approximate factorization of parabolic equations ⋮ Accuracy and stability of splitting with stabilizing corrections

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