A probabilistic-informational algorithm for approximate solution of singular integral equations. The method of reduction to Riemann-Hilbert problems

1996 ◽  
Vol 79 (6) ◽  
pp. 1411-1415
Author(s):  
O. O. Evtushenko ◽  
A. K. Prikarpats'kii ◽  
M. M. Pritula
Keyword(s):  
Approximate Solution ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations

On Projective Methods of Approximate Solution of Singular Integral Equations

1996 ◽  
Vol 3 (5) ◽  
pp. 457-474
Author(s):  
A. Jishkariani ◽  
G. Khvedelidze
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Collocation Methods ◽  
Projective Methods ◽  
Galerkin And Collocation Methods

Abstract The estimate for the rate of convergence of approximate projective methods with one iteration is established for one class of singular integral equations. The Bubnov–Galerkin and collocation methods are investigated.

scholarly journals On the approximate solution of nonlinear singular integral equations with positive index

1996 ◽  
Vol 19 (2) ◽  
pp. 389-396 ◽  
Author(s):  
S. M. Amer
Keyword(s):  
Approximate Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Jordan Curve ◽  
Singular Integral ◽  
Sufficient Conditions ◽  
Singular Integral Equations ◽  
Holder Space ◽  
Smooth Jordan Curve ◽  
Positive Index

This paper is devoted to investigating a class of nonlinear singular integral equations with a positive index on a simple closed smooth Jordan curve by the collocation method. Sufficient conditions are given for the convergence of this method in Holder space.

scholarly journals CUBIC MECHANICAL METHOD FOR THE NONLINEAR SYSTEM OF SINGULAR INTEGRAL EQUATIONS

1990 ◽  
Vol 21 (3) ◽  
pp. 201-209
Author(s):  
R. P. Eissa ◽  
M. M. Gad
Keyword(s):  
Approximate Solution ◽  
Nonlinear System ◽  
Integral Equations ◽  
Nonlinear Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Original System ◽  
Theory Of Elasticity ◽  
Discrete Operator ◽  
Mechanical Method

Many applied problems in the theory of elasticity can be reduced to the solution of singular integral equations either linear or nonlinear. In this paper we shall study a nonlinear system of singular integral equations which appear on the closed Lipanouv surface in an ideal medium [4]. We shall find a cubic mechanical method which corresponds to the system and prove its convergence; we obtained a discrete operator which corresponds to this system and study its properties and then a solution to the resulting system of the nonlinear equations which leads to an approximate solution for the original system and its convergence.

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