SOLUTION OF BOUNDARY VALUE PROBLEMS BY BROYDEN BASED SECANT METHODS.

Abstract:

All rapidly convergent methods for the solution of nonlinear equations require some derivative information. This may either be supplied explicitly by the user or built internally by the algorithm using only the values of H at the main iterates. While the latter 'secant' approach has been very successful on general problems with n less than 100 variables, it is rarely employed on the highly structured nonlinear systems arising from the discretization of differential or integral equations. In this talk it is shown that the secant idea can be adopted to the solution of two point boundary value problems as originally proposed by Hart and Soul. In particular we establish superlinear convergence estimates that are mesh independent in that they apply equivalently to the differential equation and all sufficiently fine discretizations. The talk concludes with numerical results comparing the performance of the proposed scheme to that of Newton's method.

Año de publicación:

1986

Keywords:

Fuente:

scopus