International Journal for Numerical Methods in Engineering · 1972 · 27 citations · 17 references
Natural SciencesPhysicsComputational PhysicsDifferential EquationsFluid DynamicsConvergence AnalysisFinite Difference MethodsNumerical AlgorithmsNumerical AnalysisNumerical IntegrationNumerical Methods For Differential EquationsDifferential Equation SolversFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsPoiseuille Flow
Abstract Five previously employed numerical methods for the solution of Orr–Sommerfeld problems have been compared to each other and to a new method, the differential method of near ‐orthonormalized integration. Brief summaries of each method are included. The comparison, based on seven factors, reflects the results of an implementation of a computer program for each method for the classic Orr–Sommerfeld problem of plane Poiseuille flow. This comparison shows that the new method and the algebraic finite difference method are currently the best available numerical solution methods for the problems in this class, with the new method being less problem dependent.
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The Algebraic Eigenvalue Problem
E. I., J. H. Wilkinson · Mathematics of Computation · 1966 · 5.2K citations
The Stability of Plane Poiseuille Flow
L. H. Thomas · Physical Review · 1953 · 267 citations