A hybrid parallel approach to one-parameter nonlinear boundary value problems - Domokos, Gabor; Szeberenyi, Imre (Computer Assisted Methods in Engineering and Science, 2004)
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.