A Method of Generalized Separation of Variables for Solving Three-Dimensional Integral Equations

Abstract

A method of generalized separation of variables allows to decrease complexity of a problem and to represent a solution as a series where each summand depends on every variable independently on others. This method is useful if we can't separate variables by analytic one. In that case we can get an approximate solution with desired property. The most universal method scheme is described in the Voitovich, N. N. et al., (1997). Each step of the method calculates a new member of the series and tries to make the solution of the equation more closely to exact one. In this paper we will deal with three-dimensional integral equations and method of separation of variables for solving it. This method calculates each summand of a series considering minimum of respective functional. Also some numerical results are given