Approximate solution of Volterra integral equation of first kind for special kernels
Journal of Decision Making and Healthcare, Volume 2, Issue 2, August 2025, Pages: 154–162
R. C. SINGH CHANDEL
Department of Mathematics, D. V. Postgraduate College Orai, Uttar Pradesh, 285001, India
HEMANT KUMAR
Department of Mathematics, D. A-V. Postgraduate College, Kanpur, Uttar Pradesh, 208001, India
Abstract
In the paper, we present a new approximate inversion of Volterra integral equation of first kind by using the Taylor expansión of the unknown function about lower limit of the Volterra integral. In this method, this Volterra integral equation is approximately transformed to a system of linear equations for the unknown function together with its derivatives. A desired solution can be determined by solving the resulting system according to the Cramer's rule. This method gives a simple and closed form of approximate Volterra integral equation of first kind, which may be able to use in computation work. Finally, we derive approximate solutions of this Volterra integral equation for special kernels about lower limit of Volterra integral.
Cite this Article as
R. C. Singh Chandel and Hemant Kumar, Approximate solution of Volterra integral equation of first kind for special kernels, Journal of Decision Making and Healthcare, 2(2), 154–162, 2025