XX.—Finite Hilbert Transform Technique for Triple Integral Equations with Trigonometric Kernels

1970 ◽  
Vol 68 (4) ◽  
pp. 309-321 ◽  
Author(s):  
K. N. Srivastava ◽  
M. Lowengrub
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Hilbert Transform ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Two Dimensional ◽  
Mixed Boundary Value Problems ◽  
Finite Hilbert Transform ◽  
Triple Integral Equations

In this paper, we shall be concerned with an investigation of the solution of triple integral equations involving sine and cosine kernels. These type of equations arise in the study of certain two-dimensional mixed boundary value problems in infinite planes and infinitely long strips.

scholarly journals The solution of some integral equations

1987 ◽  
Vol 29 (2) ◽  
pp. 203-215
Author(s):  
John F. Ahner ◽  
John S. Lowndes
Keyword(s):  
Wave Equation ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Laplace Equation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Fredholm Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Triple Integral Equations

AbstractAlgorithms are developed by means of which certain connected pairs of Fredholm integral equations of the first and second kinds can be converted into Fredholm integral equations of the second kind. The methods are then used to obtain the solutions of two different sets of triple integral equations tht occur in mixed boundary value problems involving Laplace' equation and the wave equation respectively.

The solution of Bessel function dual integral equations by converting to the first kind Fredholm Integral Equation: an extension of Noble’s solution

2018 ◽  
Vol 24 (8) ◽  
pp. 2536-2557
Author(s):  
S Cheshmehkani ◽  
M Eskandari-Ghadi
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Integral Transforms ◽  
Original Method ◽  
Fredholm Integral Equations ◽  
Dual Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Factor Method

In certain mixed boundary value problems, Hankel integral transforms are applied and subsequently dual integral equations involving Bessel functions have to be solved. In the literature, if possible by employing the Noble’s multiplying factor method, these dual integral equations are usually converted to the second kind Fredholm Integral Equations (FIEs) and solved either analytically or numerically, respectively, for simple or complicated kernels. In this study, the multiplying factor method is extended to convert the dual integral equations both to the first and the second kind FIEs, and the conditions for converting to each kind of FIE are discussed. Furthermore, it is shown that under some simple circumstances, many mixed boundary value problems arising from either elastostatics or elastodynamics can be converted to the well-posed first kind FIE, which may be solved analytically or numerically. Main criteria for well-posedness of FIEs of the first kind in such problems are also presented. Noble’s original method is restricted to some limited conditions, which are extended here for both first and second kind FIEs to cover a wider range of dual integral equations encountered in engineering mixed boundary value problems.

scholarly journals Dual integral equations with trigonometrical kernels

1962 ◽  
Vol 5 (3) ◽  
pp. 147-152 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
General Solution ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Dual Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Image Position

In the analysis of mixed boundary value problems in the plane, we encounter dual integral equations of the typeIf we make the substitutions cos we obtain a pair of dual integral equations of the Titchmarsh type [1, p. 334] with α = − 1, v = − ½ (in Titchmarsh's notation). This is a particular case which is not covered by Busbridge's general solution [2], so that special methods have to be derived for the solution.

Fractional Integration and Dual Integral Equations

1962 ◽  
Vol 14 ◽  
pp. 685-693 ◽  
Author(s):  
A. Erdélyi ◽  
I. N. Sneddon
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Fractional Integration ◽  
Direct Solution ◽  
Dual Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Symmetrical Form ◽  
Image Position

In the analysis of mixed boundary value problems by the use of Hankel transforms we often encounter pairs of dual integral equations which can be written in the symmetrical form(1.1)Equations of this type seem to have been formulated first by Weber in his paper (1) in which he derives (by inspection) the solution for the case in which α — β = ½, v = 0, F ≡ 1, G ≡ 0.The first direct solution of a pair of equations of this type was given by Beltrami (2) for the same values of α— β and v with G(p) ≡ 0 but with F(ρ) arbitrary.

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