Solving ODEs and DDEs with Impulses

Date of Online Publication: 31/03/2008
Keywords: Delay differential equations (DDEs); Event location; Ordinary differential, equations (ODEs); Problem solving environment (PSE); State-dependent impulses; Timedependent impulses
Authors: S.P. Corwin, S. Thompson, S.M. White
Pages: 139-149
This paper deals with the solution of systems of ordinary differential equations (ODEs) and systems of delay differential equations (DDEs) in which solution impulses are applied at specific times. Such systems include a wide range of biologically motivated examples. Event functions are used to locate the times at which impulses are applied. Systems of ODEs and especially DDEs with impulses are often difficult to solve accurately, but they can be solved quite efficiently using the event finders available in several capable solvers. The manner in which this may be accomplished is illustrated using the Matlab ODE and DDE solvers as well as the Fortran 90 ODE solver vode f90 and the Fortran 90 DDE solver dde solver. Systems with both time-dependent and with state-dependent impulses are included. The use of a GUI for vode f90 is included to illustrate the need for such GUIs for popular solvers.


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