PERTURBED CHEBYSHEV-FINITE DIFFERENCE METHOD FOR SOLVINGTHIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Authors

  • Vanenchii Peter Ayoo
    Federal University of Lafia, Nigeria
  • Esther Ngozi Enemoh
    Federal University of Lafia, Nigeria
  • Olusola Collins Akeremale
    Federal University of Lafia, Nigeria

Keywords:

Third-order ordinary differential equations , Chebyshev polynomials basis , Finite difference method , Perturbation , Legendre polynomials basis , Boundary value problems

Abstract

Ordinary differential equations are crucial in modeling complex phenomena in fluid mechanics, structural engineering, and damping systems. However, obtaining analytical solutions remains challenging due to inherent nonlinearities and intricate boundary conditions. This paper proposes a Perturbed Chebyshev Finite Difference Method (PCFDM) specifically designed to solve third-order ordinary differential equations (ODEs). The proposed framework integrates Chebyshev basis polynomials with a Legendre-based perturbation terms to enhance the approximation space and minimize truncation errors. Numerical experiments on third-order boundary value problems associated with draining and coating flows reveal that the PCFDM significantly outperforms conventional finite difference method (FDM) in terms of accuracy and computational efficiency. The results confirm that the integration of orthogonal polynomial and perturbation provides a flexible and reliable approach for solving high-order differential equations.

Author Biographies

Vanenchii Peter Ayoo

Department of Mathematics

Esther Ngozi Enemoh

Department of Mathematics,

Olusola Collins Akeremale

Department of Mathematics

Dimensions

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Published

05-05-2026

How to Cite

PERTURBED CHEBYSHEV-FINITE DIFFERENCE METHOD FOR SOLVINGTHIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS. (2026). FULafia Journal of Science and Technology , 10(2), 44-53. https://doi.org/10.62050/fjst2026.v10n2.775

Issue

Vol. 10 No. 2 (2026): Fulafia Journal of Science and Technology (FJST)

Section

Physical Sciences
Copyright & Licensing

How to Cite

PERTURBED CHEBYSHEV-FINITE DIFFERENCE METHOD FOR SOLVINGTHIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS. (2026). FULafia Journal of Science and Technology , 10(2), 44-53. https://doi.org/10.62050/fjst2026.v10n2.775

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