A Numerical Approach for Solving Second-Kind Linear and Nonlinear Volterra Integral Equations

Authors

  • Ojo Olamiposi Aduroja Department of Mathematics, University of Ilesa, Ilesa, Osun State, Nigeria. Author
  • Ganiyu Ajileye Department of Mathematics, Federal University Wukari, Taraba State, Nigeria. Author

DOI:

https://doi.org/10.62054/ijdm/0301.03

Abstract

This paper introduces a numerical method for using the collocation method to solve second-kind linear and nonlinear Volterra integral equations. Standard collocation points are used to solve the modeled problem after it is converted into an algebraic equation system. Numerical examples were utilized to evaluate the effectiveness of the approach after its uniqueness and convergence were established. The outcomes show that this approach performs better than others.

References

Abu-Ghuwaleh, M., Saadeh, R. and Qazza, A. (2022). General master theorems of integrals with applications. Mathematics, 10(19), 3547.

Adhraa M. M. and Ayal A. M. (2019). Numerical solution of linear Volterra integral equations with delay using Bernstein polynomial, International Electronic Journal of Mathematics Education, 14(3), 735-740.

Adomian, G. (2013). Solving frontier problems of physics: the decomposition method. Springer Science and Business Media.

Agbolade, A. O. and Anake, T. A. (2017). Solution of first order Volterra linear integro differential equations by collocation method, Journal of Applied Mathematics,1-5. Article ID: 1510267.doi:10.1155/2017/ 15267.

Ajileye, G., Adiku, l., Auta, J. T. Aduroja, O. O. and Oyedepo, T. (2024). Linear And Nonlinear Fredholm integro Differential Equations: An Application Of collocation Method, Journal of Fractional Calculus and Applications, 15(2), 6-16.

Al-Humedi H. O. and Shoushan A. F. (2021). Numerical solution of mixed integro-differential equations by Least-squares method and Laguerre polynomial, Earthline of Journal mathematical Sciences, 6(2), 309-323.

Djaidja, N. and Khiran, A. (2024). Approximate Solution of Linear Fredholm Integral Equation of the Second Kind Using Modified Simpson's Rule, Mathematical Modelling of Engineering Problems, 11(3), 817- 823.

Issa, K. and Saleh, F. (2017). Approximate solution of Perturbed Volterra Fredholm Integro differential equation by Chebyshev-Galerkin method. Journal of Mathematics. doi:10,1155/2017/8213932.

John. E., Asukwo, P. and Ogbonna N. (2024). Numerical Solution of Volterra Integral Equations of the Second Kind Based on Sinc Collocation Method with the Error Function, International Journal of Engineering and Mathematical Intelligence, 8(1), 11-21.

Khan, R. H. and Bakodah, H. O. (2013). Adomian decomposition method and its modification for nonlinear Abel's integral equations. Computers and Mathematics with Applications, 7, 2349-2358.

Maadadi, A. and Rahmoune, A. (2018). Numerical solution of nonlinear Fredholm Integro-differential equations using Chebyshev polynomials. International Journal of Advanced Scientific and technical Research, 8(4), 85-91. https://dx.doi.org/10.26808/rs.st.i8v4.09.

Mehdiyeva, G., Ibrahimov, V. and Imanova, M. (2019). On the Construction of the Multistep Methods to Solving the Initial-Value Problem for ODE and the Volterra Integro-Differential Equations, IAPE, Oxford, United Kingdom, ISBN: 978-1-912532-05-6.

Mirzaee, F. and Samadyar, N. (2018). On the numerical solution of stochastic quadratic integral equations via operational matrix method, Mathematical Methods in the Applied Sciences, 41(12), 4465–4479.

Parandin, N. and Gholamtabar, Sh. (2010). Numerical Solution of The Linear Fredholm Integral Equations of the Second Kind, Journal of Mathematical Extension, 5(1), 31-39.

Shoukralla, E. S. and Ahmed, B. M (2020). Numerical Solution of Volterra integral equation of the second kind using Langrange interpolation via the Vandermonde matrix, Journal of Physics: Conference Series, 1447.

Zada, L. Al-Hamami, M., Nawaz, R., Jehanzeb, S., Morsy, A., Abdel-Aty, A. and Nisar, K. S.(2021).A New Approach for Solving Fredholm Integro-Differential Equations, Information Sciences Getters, 10 (3), 3-10.

Downloads

Published

2026-03-28

How to Cite

A Numerical Approach for Solving Second-Kind Linear and Nonlinear Volterra Integral Equations. (2026). International Journal of Development Mathematics (IJDM), 3(1), 048-063. https://doi.org/10.62054/ijdm/0301.03