title: A second-order algorithm for solving dynamic cell membrane equations.
abstract: This paper describes an extension of the so-called Rush-Larsen scheme, which is a widely used numerical method for solving dynamic models of cardiac cell electrophysiology. The proposed method applies a local linearization of nonlinear terms in combination with the analytical solution of linear ordinary differential equations to obtain a second-order accurate numerical scheme. We compare the error and computational load of the second-order scheme to the original Rush-Larsen method and a second-order Runge-Kutta (RK) method. The numerical results indicate that the new method outperforms the original Rush-Larsen scheme for all the test cases. The comparison with the RK solver reveals that the new method is more efficient for stiff problems.
authors.affiliation: Simula Research Laboratory, Lysaker 1325, Norway. sundnes@simula.no
authors.forename: Joakim
authors.initials: J
authors.lastname: Sundnes
authors.forename: Robert
authors.initials: R
authors.lastname: Artebrant
authors.forename: Ola
authors.initials: O
authors.lastname: Skavhaug
authors.forename: Aslak
authors.initials: A
authors.lastname: Tveito
mesh_terms: D000465:Algorithms; D000818:Animals; D054849:Cardiac Electrophysiology / Q000379:methods*; D002462:Cell Membrane / Q000502:physiology*; D004285:Dogs; D006325:Heart Atria / Q000166:cytology; D006352:Heart Ventricles / Q000166:cytology; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D009206:Myocardium / Q000166:cytology*