SOLVING FINITE DIFFERENCE APPROXIMATIONS TO NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS BY A HOMOTOPY METHOD
1979) SOLVING FINITE DIFFERENCE APPROXIMATIONS TO NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS BY A HOMOTOPY METHOD. Technical Report CS79008-R, Computer Science, Virginia Tech. (
The Chow-Yorke algorithm is a homotopy method that has been proved globally convergent for Brouwer fixed point problems, classes of zero finding, nonlinear programming, and two-point boundary value problems. The method is numerically stable, and has been successfully applied to several practical nonlinear optimization and fluid dynamics problems. Previous application of the homotopy method to two-point boundary value problems has been based on shooting, which is inappropriate for fluid dynamics problems with sharp boundary layers. Here the Chow-Yorke algorithm is proved globally convergent for a class of finite difference approximations to nonlinear two-point boundary value problems. The numerical implementation of the algorithm is briefly sketched, and computational results are given for two fairly difficult fluid dynamics boundary value problems.
|Item Type:||Departmental Technical Report|
|Subjects:||Computer Science > Historical Collection(Till Dec 2001)|
|Deposited By:||Administrator, Eprints|
|Deposited On:||05 May 2006|