High phase-lag order trigonometrically fitted two-step Obrechkoff methods for the numerical solution of periodic initial value problems

TL;DR

This paper introduces a high-order, trigonometrically fitted two-step Obrechkoff method designed for solving periodic initial value problems, demonstrating improved efficiency, accuracy, and stability over existing methods.

Contribution

The paper develops a new symmetric two-step Obrechkoff method with algebraic order twelve and high phase-lag order specifically for periodic IVPs, outperforming recent methods.

Findings

The new method achieves higher accuracy in numerical tests.

It demonstrates superior stability compared to existing methods.

The method is more efficient for orbital and periodic problems.

Abstract

In this paper, we present the two-step trigonometrically fitted symmetric Obrechkoff methods with algebraic order of twelve. The method is based on the symmetric two-step Obrechkoff method, with 12 algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numerical results obtained by the new method for some problems show its superiority in efficiency, accuracy and stability.