Application of singular integral equations in two-dimensional problems of the theory of elasticity for piecewise-uniform bodies with cracks

1992 ◽  
Vol 62 (1) ◽  
pp. 2591-2596
Author(s):  
M. P. Savruk ◽  
N. V. Timoshchuk
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Theory Of Elasticity ◽  
Two Dimensional

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.

scholarly journals POLYNOMIAL SPLINE COLLOCATION METHOD FOR NONLINEAR TWO‐DIMENSIONAL WEAKLY SINGULAR INTEGRAL EQUATIONS

1997 ◽  
Vol 2 (1) ◽  
pp. 122-129 ◽  
Author(s):  
Arvet Pedas
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Polynomial Spline ◽  
Two Dimensional ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations

„Polynomial spline collocation method for nonlinear two‐dimensional weakly singular integral equations" Mathematical Modelling Analysis, 2(1), p. 122-129

scholarly journals ON SOLUTION OF AMPLITUDE-PHASE PROBLEM

2018 ◽  
pp. 64-68 ◽  
Author(s):  
I. V. Boykov ◽  
Ya V. Zelina
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integrals ◽  
Singular Integral Equations ◽  
Quadrature Formulas ◽  
Two Dimensional ◽  
Phase Problem ◽  
The Fourier Transform ◽  
The Hilbert Transform ◽  
Unconventional Method

The paper describes an unconventional method of solving the amplitude-phase problem. The main properties of the Hilbert transform in the discrete and continual cases for one-dimensional and two-dimensional mappings are considered. These transformations are widely used to solve amplitude-phase problem. A numerical method for solving of two-dimensional amplitudephase problem is proposed. Preliminary information about the zeros of the Fourier transform of the initial signal is not required for this method. The method is based on the apparatus of nonlinear singular integral equations. Computational schemes for solving the corresponding nonlinear singular integral equations are developed. An algorithm for finding initial values for realization of iterative methods is proposed. Quadrature formulas of the calculation of singular integrals are proposed.

scholarly journals On solution of the integral equations for the potential problems of two circular-strips

1988 ◽  
Vol 11 (4) ◽  
pp. 751-762 ◽  
Author(s):  
C. Sampath ◽  
D. L. Jain
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Potential Theory ◽  
Singular Integral ◽  
Boundary Value ◽  
Singular Integral Equations ◽  
Two Dimensional ◽  
Potential Problems ◽  
Physical Quantities ◽  
Quantities Of Interest

Solutions are given to some singular integral equations which arise in two-dimensional Dirichlet and Newmann boundary value problems of two equal infinite coaxial circular strips in various branches of potential theory. For illustration, these solutions are applied to solve some boundary value problems in electrostatics, hydrodynamics, and expressions for the physical quantities of interest are derived.

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