A generalized Chebyshev Finite Difference method for higher order boundary value problems

TL;DR

This paper introduces a generalized Chebyshev finite difference method capable of solving higher order boundary value problems with increased accuracy, extending the applicability beyond second order problems.

Contribution

It provides a new formula for derivatives of Chebyshev polynomials, enabling the method to handle higher order boundary value problems more effectively.

Findings

Results show higher accuracy than existing methods

Applicable to a wide range of higher order problems

Improved absolute error performance

Abstract

A general formula is presented for any order derivative of Chebyshev polynomials instead of the existing recursive relationship. Hence, the Chebyshev finite difference method is made applicable not only to second order problems but also to higher order boundary value problems. The generalized method is applied to a variety of higher order boundary value problems and it is seen that the obtained results are more accurate than the other numerical methods in absolute error.