Solutions of Volterra Integral Equations of Second Kind Using Various Method

  • 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/h3gtf208

    Received date: July 31, 2025

    Accepted date: October 6, 2025

    Published date: December 17, 2025

  • Volterra Integral Equation; Laplace Transform Method; Inverse Laplace Transform Method; ‎Successive Approximation Method; Variational Iterative Method

  • Abstract

    Integral equations are powerful mathematical tools used to model and solve a vast array of ‎real-world problems. Their ability to transform and simplify complex systems makes them ‎essential in theoretical and applied sciences. Volterra integral equations are essential for ‎modeling time-dependent, causal, and memory-influenced systems. They are mathematically ‎tractable and appear in a wide variety of scientific and engineering contexts. Volterra integral ‎equations appear when we convert initial value problem to an integral equation. The solution of ‎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, engineering can represent ‎mathematically in terms of volterra integral equation of first kind and second kind. We used ‎Successive approximation method; Variational iterative method and Laplace transform Method ‎for solving volterra integral equations of second kind‎.

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  • How to Cite

    Gore, T. R. ., & Khambayat , A. V. . (2025). Solutions of Volterra Integral Equations of Second Kind Using Various Method. International Journal of Basic and Applied Sciences, 14(8), 340-350. https://doi.org/10.14419/h3gtf208