Parallel multiple shooting for the solution of initial value problems

doi:10.1016/S0167-8191(06)80013-X

Parallel Computing

Volume 20, Issue 3, March 1994, Pages 275-295

https://doi.org/10.1016/S0167-8191(06)80013-X Get rights and content

Abstract

The computing time for the numerical solution of initial-value problems is closely related to the number of evaluations of the right-hand side. In general this number can only be reduced slightly on parallel computers, even if simultaneous evaluations of right-hand side are counted as one evaluation.

For special problems, however, it is possible to construct special methods which show a remarkable speedup on parallel computers. Multiple shooting, a method for boundary-value problems with an inherent parallelism, can also be applied efficiently to linear initial-value problems and to non-linear initial-value problems if good approximations are available.

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^†: Supported by the Bavarian Consortium of High Performance Scientific Computing (FORTWIHR).

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Parallel multiple shooting for the solution of initial value problems†

Abstract

J. Comp. Appl. Math.

Parallel Comput.

J. Comp. Appl. Math.

Appl. Math. Comput.

Parallel Comput.

J. Comput. Appl. Math.

On parallel methods for boundary value ODEs

Computing

Sensitivity analysis of initial-value problems with application to shooting techniques

Schwerpunktprogramm der Deutschen Forschungsgemeinschaft, Technische Universität München, Report No. 403

A relaxation strategy for the modified Newton method

Comparing numerical methods for stiff systems of ordinary differential equations

BIT