**Gábor Domokos and Imre Szeberényi**

*
corresponding author,*

Department of Strength of Materials,

This paper presents a global algorithm for parallel computers,
suitable to solve
nonlinear boundary value problems depending
on one parameter. Our method offers a mixture of
path continuation and scanning.
The former is well-known, the latter is a novel
approach introduced a few years ago, capable to
find *all *equilibria in a given domain.
The hybrid method combines the speed of path
continuation with the robustness and generality
of scanning, offering a transition between the
two methods which depends
on the choice of some characteristic control parameters.
We introduce the algorithms on a small example and test
it on large-scale problems.

- Introduction
- The basic concepts
- The Global Representation Space: variables and functions
- Construction of the simplectic grid
- Computation in one simplex

- The parallel scanning algorithm (PSA)

- The continuation algorithm

- The parallel hybrid algorithm (PHA)
- Summary and comparison of the algorithms
- Comparison of the algorithms
- Additions and generalizations
- Large-scale computations
- Implementation
- Visualization of results
- Conclusions

- Bibliography
- Appendix: Review of previously computed problems
- About this document ...

Szeberenyi Imre 2005-10-08