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Implicit-Explicit Numerical Methods in Models of Cardiac Electrical Activity

Abstract:

Mathematical models of electric activity in cardiac tissue are becoming an increasingly powerful tool in the study of the heart and cardiac arrhythmias. The ordinary differential equations con- tained within these mathematical models are challenging to solve. This challenge often means that the physiological accuracy of a model is limited by how efficient we can make the numerical solution process. In this thesis, we examine the efficiency of the numerical solution of four cardiac electrophysiological models using Implicit-Explicit (IMEX) methods. We find that a particular IMEX method, ARK5, can be up to 275 times faster than some methods most frequently used in practice.

Author: Ryan C. Dean

Advisor: Raymond J. Spiteri

Download: rdean_bsc_thesis