scholarly journals Two-dimensional singular integral equations exact solutions

1990 ◽  
Vol 31 (2) ◽  
pp. 227-232 ◽  
Author(s):  
V.A. Zisis ◽  
E.G. Ladopoulos
Keyword(s):  
Exact Solutions ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Two Dimensional

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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