Alternating Direction Implicit Methods for Parabolic Equations with a Mixed Derivative
Authors:
- Richard M. BeamRBRichard M. Beam
- R. F. WarmingRWR. F. Warming
- 1 March 1980
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific and Statistical Computing
- Vol. 1 (1) , 131-159
Abstract
Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all $A_0 $-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit $A_0 $-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.Keywords
This publication has 16 references indexed in Scilit:
- The operator compact implicit method for parabolic equationsJournal of Computational Physics, 1978
- An Implicit Factored Scheme for the Compressible Navier-Stokes EquationsAIAA Journal, 1978
- Positive Functions and some Applications to Stability Questions for Numerical Methods1978
- Comparative study of two and three level ADI methods for parabolic equations with a mixed derivativeInternational Journal for Numerical Methods in Engineering, 1976
- Error analysis for a class of methods for stiff non-linear initial value problems1976
- A linear three-level difference scheme for quasilinear parabolic equationsMathematics of Computation, 1966
- A general formulation of alternating direction methodsNumerische Mathematik, 1964
- A special stability problem for linear multistep methodsBIT Numerical Mathematics, 1963
- Survey of the stability of linear finite difference equationsCommunications on Pure and Applied Mathematics, 1956
- On the Numerical Integration of $\frac{\partial ^2 u}{\partial x^2 } + \frac{\partial ^2 u}{\partial y^2 } = \frac{\partial u}{\partial t}$ by Implicit MethodsJournal of the Society for Industrial and Applied Mathematics, 1955