A highly accurate and efficient trigonometrically-fitted P-stable three-step method for periodic initial-value problems
In this paper we present a new three-step method, which is a trigonometrically-fitted P-stable Obrechkoff method with phase-lag (frequency distortion) infinity. In this new method, we make use of higher-even-order derivatives including the eighth-order to increase the accuracy. On the other hand, we adopt a special structure to reduce the computational complexity of high-derivatives. The numerical illustration demonstrate that the new method has advantage in accuracy, periodic stability and efficiency.
obrechkoff method high-order derivative first-order derivative formula second-order initial value problem with periodic solutions numerical solution to the duffing equation