Trigonometrically-Fitted Simpson’s Method for Solving Volterra Integro-Differential Equations

  • R. A. Olowe Department of Mathematics, University of Lagos, Akoka, Nigeria.
  • O. A. Akinfenwa Department of Mathematics, University of Lagos, Nigeria
  • R. I. Abdulganiy Distance Learning Institute, University of Lagos, Akoka, Nigeria.
  • S. A. Okunuga Department of Mathematics, University of Lagos, Akoka, Nigeria.
DOI: https://doi.org/10.6084/m9.figshare.22015772
Keywords: Volterra integro-differential equations (VIDEs), block methods, continuous method, Leibnitz rule, Trigonometrically fitted methods

Abstract

In this study, a third derivative trigonometrically fitted Simpson’s method is developed and
applied to approximate the solution of Volterra Integro-Differential Equations (VIDEs) via the multistep collocation method. The VIDEs are first transformed to IVPs by the Leibnitz rule of differentiating integral. A continuous third derivative trigonometrically fitted method is constructed with the trigonometric basis function from which both the main and the complementary discrete formulas are generated. The two discrete formulas are then applied as simultaneous integrators in a block by block form to solve the VIDEs. Whereas numerical properties of the proposed method are investigated, its accuracy is demonstrated through some standard examples.

Published
2023-01-22
How to Cite
Olowe, R. A., Akinfenwa, O. A., Abdulganiy, R. I., & Okunuga, S. A. (2023). Trigonometrically-Fitted Simpson’s Method for Solving Volterra Integro-Differential Equations. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 8(2), 68 - 78. https://doi.org/10.6084/m9.figshare.22015772
Issue
Vol 8 No 2 (2022)
Section
Articles

Copyright (c) 2023 R. A. Olowe, O. A. Akinfenwa, R. I. Abdulganiy, S. A. Okunuga

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