Theory of splineinteration methos of comuter physiks. Part II. Methods of solving nonlinerar integra lequations
© Starkov V.N.
The construction of splineiteration methods of the solution of linear integral equations features a uniform character, which makes it possible to apply it to different nonlinear integral equations. In the second part of the work splineiteration methods of the solution of the Uryson and UrysonVolterra integral equations proposed and justified. The principal theorem concerning splinequadrature for nonlinear integral equations similar to the Vaynikko theorem is formulated and proved. The splineiteration method of the solution of the Volterra linear integral equations of the second kind is generalized for for the Volterra nonlinear equations. Various versions of combination of the splinequadrature method and the NewtonKantorovich method for the solution of nonlinear integral equations are described. Splineiteration methods elaborated for the solution of the nonlinear integral equations have been generalized for the case of the twodimensional Uryson equation and the twodimensional Volterra nonlinear equation. <<back 
