Numerical Methods For Solution of Di fferential Equations

Tobias Ritschel

AbstractRunge-Kutta methods are used to numerically approximate solutions to initial value problems, which may be used to simulate, for instance, a biological system described by ordinary differential equations. Simulations of such system may be used to test di fferent control strategies and serve as an inexpensive alternative to real-life testing.
In this thesis a toolbox is developed in C and Matlab containing e ffective numerical Runge-Kutta methods. Testing thse methods on the time it takes to
simulate a system for a large set of parameters showed that some methods performed well in some cases whereas others were faster in others such that not one method outbested the others. Carrying out the same tests using parallel simulations showed that a speed-up of between 11 and 12 is possible in Matlab and in C when using 12 processes, and that di fferent implementations of parallel simulations in C, are suitable for di fferent number of processes.
In all aspects, simulations were obtained much faster in C compared to Matlab.
TypeBachelor thesis [Academic thesis]
PublisherTechnical University of Denmark, DTU Compute, E-mail:
AddressMatematiktorvet, Building 303-B, DK-2800 Kgs. Lyngby, Denmark
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IMM Group(s)Scientific Computing