Abstract
The paper is concerned with the applicability of the collocation method to a class of nonlinear singular integral equations with a Carleman shift preserving orientation on simple closed smooth Jordan curve in the generalized Holder space Hφ(L).
Highlights
Nonlinear singular integral equations are widely used and connected with applications in several field of engineering mechanics like structural analysis, fluid mechanics and aerodynamics. This leads to the necessity to derive solutions for the nonlinear singular integral equations arising in applications, by using some approximate and constructive methods
The theory of nonlinear singular integral equations with Hilbert and Cauchy kernel and its related Riemann-Hilbert problems have been developed in works of Pogorozelski W. [20], Guseinov A
Existence results and approximate solutions have been studied for nonlinear singular integral equations (NSIE) and nonlinear singular integral equations with shift (NSIES) by many authors among them we mention (1-6, 10,11,15,16,19,21)
Summary
Nonlinear singular integral equations are widely used and connected with applications in several field of engineering mechanics like structural analysis, fluid mechanics and aerodynamics. This leads to the necessity to derive solutions for the nonlinear singular integral equations arising in applications, by using some approximate and constructive methods, (see [16] ). The successful development of the theory of singular integral equations (SIE) naturally stimulated the study of singular integral equations with shift (SIES). Existence results and approximate solutions have been studied for nonlinear singular integral equations (NSIE) and nonlinear singular integral equations with shift (NSIES) by many authors among them we mention (1-6, 10,11,15,16,19,21).
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