A modified Gautschi’s method without order reduction when integrating boundary value nonlinear wave problems

Abstract

In this paper we analyse the order reduction which turns up when integrating nonlinear wave problems with non-homogeneous and time-dependent boundary conditions with the well-known Gautschi’s method. Moreover, a technique is suggested to avoid that order re- duction so that the classical local order 4 and global order 2 are recovered. On the other hand, the usual approximation for the derivative which is used together with this method is also analysed and a substantial improvement is suggested. Some numerical results are shown which corroborate the performed analysis.