The bidomain and monodomain models describing cardiac electrophysiology are computationally demanding to solve. Employing efficient numerical methods is therefore important for the practical use of these models. In this thesis we have explored the efficiency of numerical methods based on finite elements in space and explicit and semi-implicit finite differences in time. The explicit scheme which solves the bidomain equations uses a fixed number of Jacobi-iterations to solve the stationary, elliptic part of the model. The results show that an explicit scheme based on Jacobi iterations can give comparable and, in some cases, better computational efficiency than semi-implicit schemes based on operator splitting.