Geophysical Journal | 2002 volume 24 5

Theory of spline-interation methos of comuter physiks. Part II. Methods of solving non-linerar integra lequations

© Starkov V.N.

The construction of spline-iteration 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 spline-iteration methods of the solution of the Uryson and Uryson-Volterra integral equations proposed and justified. The principal theorem concerning spline-quadrature for nonlinear integral equations similar to the Vaynikko theorem is formulated and proved. The spline-iteration 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 spline-quadrature method and the Newton-Kantorovich method for the solution of nonlinear integral equations are described. Spline-iteration methods elaborated for the solution of the nonlinear integral equations have been generalized for the case of the two-dimensional Uryson equation and the two-dimensional Volterra nonlinear equation.

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