SIAM Journal on Numerical Analysis · 1973 · 137 citations · 9 references
ComputingComputational EngineeringPhysicsComputational MechanicsDifferential EquationsFinite Element AnalysisConvergence AnalysisFinite Difference MethodsIterative SolversNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsDifferential Equation SolversElliptic Partial Differential EquationsFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsParabolic Partial Differential Equations
A general formulation of the additive correction methods of Poussin [4] and Watts [7] is presented. The methods are applied to the solution of finite difference equations resulting from elliptic and parabolic partial differential equations. A new method is developed for anisotropic and heterogeneous problems. For such difficult problems the method presented here is comparable with Stone’s strongly implicit method, while all other methods tested require much greater computational effort. The correction approach discussed here can be easily applied with any iterative method.
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