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Research Article Open access CC BY 4.0

Hermite Polynomial-based Methods for Optimal Order Approximation of First-order Ordinary Differential Equations

J. K. Odeyemi, O. O. Olaiya, F. O. Ogunfiditimi

Journal of Advances in Mathematics and Computer Science · pp. 16–32 · Published 25 Mar 2023

10.9734/jamcs/2023/v38i61765

Abstract

This study investigates the continuous linear multistep techniques utilized for solving first-order initial value problems in ordinary differential equations. Specifically, the study focuses on step k = 9, utilizing Hermite polynomials as basis functions. This study effectively constructs the Adams-Bashforth, Adams-Moulton, and optimal order methods by applying collocation and interpolation methodologies. The methods are thoroughly examined using various numerical instances to demonstrate their efficacy and validity. Notably, the optimal order method exhibits superior accuracy and efficiency compared to the traditional Adams-Bashforth and Adams-Moulton methods. The research results contribute novel and improved methodologies for solving initial value problems in differential equations, which have extensive applications across diverse mathematical and scientific domains.

Continuous linear multistep methods hermite polynomials adams-Bashforth adams-moulton q-step method

References (5)

  1. 1 A four-point fully implicit method for the numerical integration of third-order ordinary differential equations [DOI]
  2. 2 Orthogonal polynomials [DOI]
  3. 3 Derivation of Continuous Linear Multistep Methods Using Hermite Polynomials as Basis Functions [DOI]
  4. 4 Numerical solution of Black-Scholes Partial Differential Equation using Direct solution of second-order Ordinary Differential Equation with two-step hybrid Block Method of Order seven.
  5. 5 International Journal of Engineering Research and Applications [DOI]

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