A 5(4) Embedded Pair of Explicit Trigonometrically-Fitted Rungea??Kuttaa??Nystr??m Methods for the Numerical Solution of Oscillatory Initial Value Problems

摘要

A 5(4) pair of embedded explicit trigonometrically-fitted Rungea??Kuttaa??Nystr??m (EETFRKN) methods especially designed for the numerical integration of second order initial value problems with oscillatory solutions is presented in this paper. Algebraic order analysis and the interval of absolute stability for the new method are also discussed. The new method is capable of integrating the test equation y a?3 = a?? w 2 y . The new method is much more efficient than the other existing Rungea??Kutta and Rungea??Kuttaa??Nystr??m methods.