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Published in:
2006 | OriginalPaper | Chapter
Solving Systems of ODEs
Authors : Joakim Sundnes, Glenn Terje Lines, Xing Cai, Bjørn Fredrik Nielsen, Kent-Andre Mardal, Aslak Tveito
Published in: Computing the Electrical Activity in the Heart
Publisher: Springer Berlin Heidelberg
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The operator splitting algorithms introduced in Chapter 3 reduced the solution of the bidomain equations to solving linear PDE systems and nonlinear systems of ODEs. Techniques for discretizing the PDE system were presented in Chapter 3, while techniques for solving the resulting linear systems were discussed in Chapter 4. What remains to have a complete computational method for the bidomain model is to find an efficient method for solving the nonlinear ODE systems. Note that the spatial discretization of the bidomain equations results in one ODE system for each node in the finite element grid. Realistic simulations may require several millions of nodes, and it is therefore of the utmost importance to solve the ODE systems efficiently.