One of the leading experts in the field discusses recent developments in the numerical analysis of nonlinear equations involving a finite number of parameters, and shows how these equations can be developed on a differential geometric basis. Topics include equilibrium manifolds, path-tracing on manifolds, aspects of computational stability analysis, discretization errors of parameterized equations, and computational error assessment and related questions.
Table of Contents
Some Sample Problems.
Some Background Material.
Solution Manifolds and Their
One-Distributions and Augmented Equations.
A Continuation Method.
Some Numerical Examples.
The Computation of Limit Points.
Differential Equations on Manifolds.
Error Estimates and Related Topics.