Spectral Monic Chebyshev Approximation for Higher Order Differential Equations

TL;DR

This paper introduces a spectral method using Monic Chebyshev polynomials for directly solving higher-order boundary value problems, avoiding the need to reduce them to lower-order systems, and demonstrates its efficiency and accuracy through examples.

Contribution

The paper presents a novel spectral method based on Monic Chebyshev polynomials for directly solving higher-order boundary value problems without reduction to lower-order equations.

Findings

Method is efficient for solving HBVPs.

Method achieves high accuracy in examples.

Applicable to a wide range of HBVPs.

Abstract

This paper is focused on performing a new method for solving linear and nonlinear higher-order boundary value problems (HBVPs). This direct numerical method based on spectral method. The trial function of this method is the Monic Chebyshev polynomials (MCPs). This method was relying on derivative of MCPs which explicit in the series expansion. The advantage of this method is solved HBVPs without transforming it to a system of lower-order ordinary differential equations (ODEs). This method supported by examples of HBVPs in wide application. The mentioned examples showed that the proposed method is efficient and accurate.