Numerical Methods for Singular Perturbation Problems.
NAVAL UNDERWATER SYSTEMS CENTER NEWPORT RI
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Singular perturbation equations contain many of the essential difficulties of the Navier-Stokes equations. In this report the weighted-mean scheme for linear equations and the monotone difference scheme for nonlinear equations were adopted. Presented here are fast iterative techniques for solving large systems of equations that result from discretization. Numerical results are also presented for nonlinear cases using Newtons method combined with the minimal residual method. The main conclusions are that minimal residual methods with a preconditioning technique and multigrid methods with a special relaxation scheme have proved to be quite reliable and far more efficient than standard iterative methods. Author
- Theoretical Mathematics