A methodology for the generation of low-cost higher-order methods for linear dynamics

This work presents a methodology which generates e cient higher-order methods for linear dynamics by improving the accuracy properties of NHrsett methods towards those of Pad e methods. The methodology is based on a simple and low-cost iterative procedure which is used to implement a set of higher-order methods with controllable dissipation. A sequence of improved solutions is obtained which correspond to algorithms o ering an e ective compromise between the e ciency of N rsett methods and the accuracy of Pad e methods. Moreover, a direct control over high-frequency dissipation is possible by means of an algorithmic parameter. Numerical tests are reported which con rm that this set of algorithms is really attractive for linear dynamic analysis