Volterra equations and applications

In this study, the solution methods of Volterra equations were analysed.After the introduction part, in the second section the general information about Volterra equationswere presented. This information consist of resolution in Volterra equation, solving the resolution bymeans of differantial equation and the basic successive substitute approximations method. Also, in thesolution of Volterra equations the rules of Leibnitz was used as another method. The solution ofintegral equtaion, which was turned into differantial equations, was acquired through this rule. In thefirst type of Volterra equations Laplace transformation method, Gamma-Beta functions and theirsolution methods were analysed. Here, first type of Volterra equation was solved by not reducing tothe equation into the second type. However, in the type of volterra equations the approximationsmethods of Runge-Kutta and Neumann were used. In this part it was indicated that an equation isacquired by not condensing upon the function of K(x,t). This equation is a method for the solution ofan integral equation.In the third section, the examples about these methods were solved.When we come to the fourth section, it was analysed the numerical solutions of Volterra equations bytaking into consideration the flexibility problem of homogenous chord. Firsly, the general solution wascalculated by analysing the starting conditions of differantial equation which is not homogenous inVolterra-Fredholm and Fredholm integral equation. By using these findings the solution was acquiredby the basic successive substitute approximations method and modified successive approximationsmethod. These solutions were determined for the values of t=0, 0.1, 0.2,.....1.Key words: The operator of Fredholm, the operator of Volterra.