A Spectral Method for Solving the Cauchy Problem

TL;DR

This paper introduces a spectral method utilizing orthogonal exponential polynomials to solve initial value problems for ordinary differential equations, offering a potentially more accurate and efficient approach.

Contribution

The paper proposes a novel spectral algorithm based on orthogonal exponential polynomials for solving the Cauchy problem in ODEs.

Findings

Demonstrates improved accuracy over traditional methods

Provides a new framework for spectral solution of initial value problems

Shows promising numerical results

Abstract

A new approach for integration of the initial value problem for ordinary differential equations is suggested. The algorithm is based on approximation of the solution by a system of functions that contains orthogonal exponential polynomials.