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Domain decomposition methods for solving the Burgers equation

Robert Cimrman (1999)

Applications of Mathematics

This article presents some results of numerical tests of solving the two-dimensional non-linear unsteady viscous Burgers equation. We have compared the known convergence and parallel performance properties of the additive Schwarz domain decomposition method with or without a coarse grid for the model Poisson problem with those obtained by experiments for the Burgers problem.

Hermite pseudospectral method for nonlinear partial differential equations

Ben-yu Guo, Cheng-long Xu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Hermite polynomial interpolation is investigated. Some approximation results are obtained. As an example, the Burgers equation on the whole line is considered. The stability and the convergence of proposed Hermite pseudospectral scheme are proved strictly. Numerical results are presented.

Including eigenvalues of the plane Orr-Sommerfeld problem

Peter P. Klein (1993)

Applications of Mathematics

In an earlier paper [5] a method for eigenvalue inclussion using a Gerschgorin type theory originating from Donnelly [2] was applied to the plane Orr-Sommerfeld problem in the case of a pure Poiseuile flow. In this paper the same method will be used to deal Poiseuile and Couette flow. Potter [6] has treated this case before with an approximative method.

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