A second-derivative functionally fitted method of maximal order for oscillatory initial value problems.

Abstract

[EN]This paper deals with the construction of a functionally fitted method for solving first-order differential systems whose solutions present an oscillatory behaviour. The method incorporates the second derivative to obtain better accuracies and is developed on the basis that it provides no errors when the true solution is a linear combination of some trigonometric and exponential functions containing a parameter. The main properties of the method are presented, showing a fourth-order convergence. Some numerical experiments are included to show the good performance of the proposed method.