Numerical Solutions of Third Kind Volterra Integral Equations Using Simpson’s Rule

  • Authors

    • Tejal R. Gore Research Scholar, Department of Mathematics, Sandip University, Nashik
    • Avinash V. Khambayat Professor, Department of Mathematics, Sandip University, Nashik
    https://doi.org/10.14419/gq7zz405

    Received date: July 31, 2025

    Accepted date: September 30, 2025

    Published date: November 23, 2025

  • Volterra Integral equation; Simpson's 1/3 rd Rule; Simpson's 3/8 th Rule

  • Abstract

    Volterra integral equations appear when we convert an initial value problem to an integral ‎equation. The solution of the Volterra integral equation is much easier than the original initial value ‎problem. Many problems of thermodynamics, biology, chemistry, medical sciences, physics, ‎heat flow, neutron diffusion problem, electric circuit problem, transform problem mechanics, ‎and engineering can be represented mathematically in terms of Volterra integral equations of the first and ‎second kind. Numerical Method for solving Third Kind Volterra Integral Equations (VIEs) ‎using Simpson's Rule. By approximating the unknown function using Lagrange Polynomial ‎interpolation and applying Simpson's rule for numerical integration, we obtain a system of ‎linear algebraic equations. The solution of this system provides an approximation to the ‎original integral equation‎.

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  • How to Cite

    Gore , T. R. ., & Khambayat, A. V. . (2025). Numerical Solutions of Third Kind Volterra Integral Equations Using Simpson’s Rule. International Journal of Basic and Applied Sciences, 14(7), 520-526. https://doi.org/10.14419/gq7zz405