ABSTRACT
Any equation in which the unknown function appears under the integral sign is called an integral equation. Nonlinear differential equations can also be transformed into integral equations. In fact this is one method used to establish properties of the equation and to develop approximate and numerical solutions. If the unknown function appears in the equation in any way other than to the first power then the integral equation is said to be nonlinear. Only the simplest integral equations can be solved exactly. Usually approximate or numerical methods are employed. The advantage is that integration is a “smoothing operation,” whereas differentiation is a “roughening operation”. The special convolution equation is a special case of the Volterra equation.
