On the solution of integral equations by the method of integral transforms

1970 ◽  
Vol 10 (6) ◽  
pp. 1034-1042 ◽  
Author(s):  
V. N. Strakhov
Keyword(s):  
Integral Equations ◽  
Integral Transforms

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.

On Steady-State Filtration of Fluid in Strip-Like and Wedge-Shaped Porous Ground Bases

2014 ◽  
Vol 1020 ◽  
pp. 373-378
Author(s):  
Suren M. Mkhitaryan ◽  
H.V. Tokmajyan ◽  
S.A. Avetisyan ◽  
M.S. Grigoryan
Keyword(s):  
Steady State ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Vertical Velocity ◽  
Boundary Value ◽  
Integral Transforms ◽  
Plane Boundary ◽  
Filtration Theory

In statement of the steady-state filtration theory and within the framework of the Darcy`s law plane boundary value problems for the strip-like and wedge-shaped porous ground base are considered when through some system of segments on one face of the base the fluid with a certain vertical velocity or with a certain pressure is injected inside the base. These solutions are reduced to integral equations by means of integral transforms.

scholarly journals Aboodh and Mahgoub Transform in Boundary Value Problems of System of Ordinary Differential Equations

2021 ◽  
pp. 67-75
Author(s):  
Dr. D. P. Patil
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Boundary Value ◽  
Integral Transforms

Integral transforms plays important role in solving differential equations and integral equations. In this paper we discuss application of Aboodh transform and Mahgoub transform in solving boundary value problem of system of ordinary differential equations and result shows that Aboodh transform and Mahgoub transform are closely connected.

Ian Naismith Sneddon, O.B.E. 8 December 1919 – 4 November 2000

2002 ◽  
Vol 48 ◽  
pp. 417-437 ◽  
Author(s):  
P. Chadwick
Keyword(s):  
World War Ii ◽  
Integral Equations ◽  
Linear Theory ◽  
Analytical Techniques ◽  
Integral Transforms ◽  
Theory Of Elasticity ◽  
World War ◽  
Dual Integral Equations ◽  
Cultural Life ◽  
The University

Ian Sneddon was introduced to problems in the linear theory of elasticity involving the indentation of a surface and the extension of a crack through his work for the Ministry of Supply during World War II. He maintained a lifelong research interest in this area and also made distinguished contributions to a range of related analytical techniques, notably the application of integral transforms and the solution of dual integral equations. His many books, extensive travels and engaging personality made him very well known internationally, and he developed particularly fruitful contacts in the USAand Poland. He gave devoted service to the University of Glasgow, where the bulk of his career was spent, and played an active part in the cultural life of Scotland.

scholarly journals New Inversion Techniques for Some Integral Transforms via the Generalized Product Theorem of the Mellin Transform

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Alireza Ansari ◽  
Mohammadreza Ahmadi Darani
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Mellin Transform ◽  
Singular Integral Equations ◽  
Integral Transforms ◽  
Product Theorem ◽  
Inversion Techniques

We introduce the generalized product theorem for the Mellin transform, and we solve certain classes of singular integral equations with kernels coincided with conditions of this theorem. Also, new inversion techniques for the Wright, Mittag-Leffler, Stieltjes, and Widder potential transforms are obtained.

scholarly journals On certain methods of solving a class of integral equations of Fredholm type

1992 ◽  
Vol 52 (1) ◽  
pp. 1-10 ◽  
Author(s):  
H. M. Srivastava ◽  
R. K. Raina
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Mellin Transform ◽  
Integral Transforms ◽  
Fredholm Type ◽  
Reduction Techniques ◽  
Hypergeometric Integral ◽  
Type Integral ◽  
Interesting Generalization

AbstractThe authors begin by presenting a brief survey of the various useful methods of solving certain integral equations of Fredholm type. In particular, they apply the reduction techniques with a view to inverting a class of generalized hypergeometric integral transforms. This is observed to lead to an interesting generalization of the work of E. R. Love [9]. The Mellin transform technique for solving a general Fredholm type integral equation with the familiar H-function in the kernel is also considered.

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