Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations

TL;DR

This paper presents an efficient implementation of RKN-type Fourier collocation methods for second-order differential equations, utilizing alternative and blended formulations to enhance performance, validated through numerical tests.

Contribution

It introduces a novel implementation approach for RKN-type Fourier collocation methods, improving efficiency and effectiveness for solving second-order differential equations.

Findings

Implementation is more efficient than traditional methods.

Numerical tests confirm the effectiveness of the proposed approach.

The methods perform well on benchmark problems.

Abstract

In this paper we discuss the efficient implementation of RKN-type Fourier collocation methods, which are used when solving second-order differential equations. The proposed implementation relies on an alternative formulation of the methods and the blended formulation. The features and effectiveness of the implementation are confirmed by the performance of the methods on two numerical tests.