APPROXIMATE SOLUTION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR INTEGRO-DIFFERENTIAL EQUATION OF CONVOLUTION TYPE
In the space cone of continuous functions on the positive semiaxis, the boundary value problem for integro-differential equation of the Volterer type with a difference kernel and power nonlinearity is studied. Accurate a priori estimates were obtained for solutions of the problem under consideration, which made it possible to prove the global theorem on the existence and uniqueness of the solution. It is shown that the solution can be found by the method of successive approximations of the Picard type, for which estimates of error and speed of their convergence to the exact solution are indicated. The study is based on the reduction of this integro-differential equation to an equivalent nonlinear integral equation. Examples illustrating the results are given.