Exploiting special problem structure when reliably investigating the solution of systems of IVPs and DDEs

In recent years we have developed a class of reliable order p methods for the approximate solution of general systems of initial value problems (IVPs) and delay differential equations (DDEs). In the theoretical analysis of these methods we have identified several trade-offs that do arise and have to...

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Bibliographic Details
Main Author: Enright, W. H.
Format: Conference Proceeding
Language:English
Subjects:
Approximation
Boundary value problems
Differential equations
Identification methods
Tradeoffs
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Summary:In recent years we have developed a class of reliable order p methods for the approximate solution of general systems of initial value problems (IVPs) and delay differential equations (DDEs). In the theoretical analysis of these methods we have identified several trade-offs that do arise and have to be addressed when applying these methods to problems that exhibit special structure. Similar trade-offs also arise when one is concerned with investigating other important properties of the solutions. We will give examples of such trade-offs that arise when investigating the sensitivities of the solutions, and when very accurate approximate solutions are required.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4951747