Abstract:
Runge-Kutta methods for the numerical solution of ordinary differential equations (ODEs) and the extension to stochastic differential equations (SDEs) are presented. The Butcher rooted-tree theory used for the derivation of order conditions for ODEs and its generalization to coloured trees for SDEs are discussed. The results of numerical experiments on linear and nonlinear problems with several explicit numerical methods with weak orders 1 and 2 are presented.