A method of generalized separation of variables for solving two-dimensional integral equations

摘要

The concept of separation of variables traditionally unites with the Fourier method of solving of differential equations in partial derivatives. The most universal scheme of its many generalizations is described by Kaleniuk et al. (1993). Its main idea consists of a choice of a problem partial solution with a more complicated structure. In the solution of many-dimensional integral equations a different variational-iterative generalization of variables separation is used. The solution is obtained approximately in the form of a series. The members of this series are functions with separated variables. They are calculating successively to satisfy the condition of minimization of corresponding functionals. Each new step of the method permits one to calculate a new member of the series and also makes the solution of the equation accurate. In this paper the method of the generalized separation of variables for solving a two-dimensional integral equation is set forth, its particle basis is examined, and some numerical results are shown.