Different iterative schemes based on collocation methods have been well studied and widely applied to the numerical solution of nonlinear hypersingular integral equations (Capobianco et al. 2005). In this paper we apply Newton's method and its modified version to solve the equations obtained by applying a collocation method to a nonlinear hypersingular integral equation of Prandtl's type. The corresponding convergence results are derived in suitable Sobolev spaces. Some numerical tests are also presented to validate the theoretical results.
Newton methods for a class of nonlinear hypersingular integral equations
Capobianco MR;
2010
Abstract
Different iterative schemes based on collocation methods have been well studied and widely applied to the numerical solution of nonlinear hypersingular integral equations (Capobianco et al. 2005). In this paper we apply Newton's method and its modified version to solve the equations obtained by applying a collocation method to a nonlinear hypersingular integral equation of Prandtl's type. The corresponding convergence results are derived in suitable Sobolev spaces. Some numerical tests are also presented to validate the theoretical results.File in questo prodotto:
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