APPROXIMATE SOLUTION OF VOLTERRA INTEGRAL EQUATION OF FIRST KIND FOR SPECIAL KERNELS

In the paper, we present a new approximate inversion of Volterra integral equation of first kind by using the Taylor expansin 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.