Section: New Results

High-order integration methods for ion channel models

On November 15, 2017, C. Douanla Lontsi defended his PhD thesis [9] on the numerical analysis of time-stepping methods for the cardiac monodomain equations. A huge amount of work was carried out in the thesis. The thesis builds on the seminal Rush-Larsen technique [62], [57], and the recent novel computational interest in exponential integrator methods. Two new exponential methods of arbitrarily high order are proposed (EABk and RLk). Most notably, Rush-Larsen techniques of order $k=2,3,4$ were entirely explicited. The theory was adapted to analyse these methods and convergence proofs were derived. The complete Dahlquist stability region of these methods was documented. Finally, the methods were integrated into an IMEX strategy to solve the monodomain equation in 1D to 3D problems, with two ionic models (BR and TNNP). The results essentially show that order at least 3 is required to leas to reasonably accurate simulations. Three journal papers were submitted in 2017, [39], [41], [40].