DEVELOPMENT AND ANALYSIS OF AN INTEGRATOR METHOD FOR THE SOLUTION OFORDINARY DIFFERENTIAL EQUATIONS VIA THE COMBINATION OF TRIGONOMETRIC,EXPONENTIAL AND POLYNOMIAL BASIS FUNCTIONS

Authors

  • Sunday Emmanuel Fadugba
  • Taiwo Eniola Fayode
    Bamidele Olumilua University of Education Science and Technology Ikere-Ekiti Ekiti-State
  • Yetunde Omolara Oniyinde
  • Victor Oluwatobi Abifade
  • Olubode Oludare Bamisile
  • Joseph Temitope Okunlola
  • Malesela C. Kekana
  • Ayodele Oluwasola Joshua

Abstract

In this paper, we present a new numerical integrator for solving first-order initial value problems in ordinary differential equations (ODEs). The method is developed using a combination of trigonometric, exponential, and polynomial basis functions, allowing it to effectively capture different types of solution behaviour, including oscillatory and rapidly varying patterns. The scheme is derived through an interpolation approach, resulting in a simple and efficient one-step method. The main properties of the method were carefully examined, and it was shown to be third-order accurate, consistent, and zero-stable, which confirmed the convergence of the method. A linear stability analysis further reveals that the method is conditionally stable. To ascertain its performance, the method is applied to five test problems involving linear and nonlinear ordinary differential equations. The numerical results show that the errors decrease as the step size ℎ decreases. The proposed method provides a reliable and practical tool for solving initial value problems in ODEs, and it offers a good balance between accuracy and computational efficiency. Further work may extend the method to more complex and stiff systems.

Author Biographies

Sunday Emmanuel Fadugba

Department of Mathematics

Taiwo Eniola Fayode

Department of Mathematical Sciences

Yetunde Omolara Oniyinde

Department of Mathematical Sciences 

Victor Oluwatobi Abifade

Department of Mathematical Sciences

Olubode Oludare Bamisile

Department of Basic Sciences (Mathematics)

Joseph Temitope Okunlola

Department of Mathematical and Physical Sciences

Malesela C. Kekana

Department of Mathematics and Statistics

Ayodele Oluwasola Joshua

Department of Mathematical Sciences

Dimensions

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Published

28-10-2026

How to Cite

DEVELOPMENT AND ANALYSIS OF AN INTEGRATOR METHOD FOR THE SOLUTION OFORDINARY DIFFERENTIAL EQUATIONS VIA THE COMBINATION OF TRIGONOMETRIC,EXPONENTIAL AND POLYNOMIAL BASIS FUNCTIONS. (2026). FULafia Journal of Science and Technology , 11(1), 31-41. https://doi.org/10.62050/fjst2027.v11n1.897

Issue

Vol. 11 No. 1 (2027): Fulafia Journal of Science and Technology (FJST)

Section

Physical Sciences
Copyright & Licensing

How to Cite

DEVELOPMENT AND ANALYSIS OF AN INTEGRATOR METHOD FOR THE SOLUTION OFORDINARY DIFFERENTIAL EQUATIONS VIA THE COMBINATION OF TRIGONOMETRIC,EXPONENTIAL AND POLYNOMIAL BASIS FUNCTIONS. (2026). FULafia Journal of Science and Technology , 11(1), 31-41. https://doi.org/10.62050/fjst2027.v11n1.897

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