Solution of Fredholm-Volterra Integral Equation of the Second Kind in Series Form

2004 ◽  
Vol 4 (4) ◽  
pp. 537-538
Author(s):  
A.A. El -Bary .
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Series Form ◽  
In Series

Solving Volterra integral equation by using a new transformation

2021 ◽  
Vol 24 (3) ◽  
pp. 735-741
Author(s):  
Sahar Muhsen Jaabar ◽  
Ahmed Hadi Hussain
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation

On approximate solutions of the generalized Volterra integral equation

2014 ◽  
Vol 20 ◽  
pp. 59-66 ◽  
Author(s):  
Anna Bahyrycz ◽  
Janusz Brzdȩk ◽  
Zbigniew Leśniak
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Approximate Solutions

scholarly journals XXV.—The Generating Function of the Reciprocal of a Determinant

1905 ◽  
Vol 40 (3) ◽  
pp. 615-629
Author(s):  
Thomas Muir
Keyword(s):  
Generating Function ◽  
Specific Character ◽  
Partial Fraction ◽  
Homogeneous Functions ◽  
Series Form ◽  
General Proposition ◽  
In Series ◽  
Image Position ◽  
The Given

(1) This is a subject to which very little study has been directed. The first to enunciate any proposition regarding it was Jacobi; but the solitary result which he reached received no attention from mathematicians,—certainly no fruitful attention,—during seventy years following the publication of it.Jacobi was concerned with a problem regarding the partition of a fraction with composite denominator (u1 − t1) (u2 − t2) … into other fractions whose denominators are factors of the original, where u1, u2, … are linear homogeneous functions of one and the same set of variables. The specific character of the partition was only definable by viewing the given fraction (u1−t1)−1 (u2−t2)−1…as expanded in series form, it being required that each partial fraction should be the aggregate of a certain set of terms in this series. Of course the question of the order of the terms in each factor of the original denominator had to be attended to at the outset, since the expansion for (a1x+b1y+c1z−t)−1 is not the same as for (b1y+c1z+a1x−t)−1. Now one general proposition to which Jacobi was led in the course of this investigation was that the coefficient ofx1−1x2−1x3−1…in the expansion ofy1−1u2−1u3−1…, whereis |a1b2c3…|−1, provided that in energy case the first term of uris that containing xr.

The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid

1966 ◽  
Vol 33 (1) ◽  
pp. 68-74 ◽  
Author(s):  
Joseph F. Shelley ◽  
Yi-Yuan Yu
Keyword(s):  
Stress Field ◽  
Uniaxial Tension ◽  
Elastic Solid ◽  
Displacement Function ◽  
Hydrostatic Tension ◽  
Series Form ◽  
Spherical Inclusions ◽  
Spherical Cavities ◽  
In Series ◽  
The Common

Presented in this paper is a solution in series form for the stresses in an infinite elastic solid which contains two rigid spherical inclusions of the same size. The stress field at infinity is assumed to be either hydrostatic tension or uniaxial tension in the direction of the common axis of the inclusions. The solution is based upon the Papkovich-Boussinesq displacement-function approach and makes use of the spherical dipolar harmonics developed by Sternberg and Sadowsky. The problem is closely related to, but turns out to be much more involved than, the corresponding problem of two spherical cavities solved by these authors.

On the Volterra integral equation relating creep and relaxation

2008 ◽  
Vol 24 (3) ◽  
pp. 035009 ◽  
Author(s):  
R S Anderssen ◽  
A R Davies ◽  
F R de Hoog
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation

Application of Simpson's method for solving singular Volterra integral equation

2021 ◽  
Vol 9 (4) ◽  
pp. 206-215
Author(s):  
Mustapha YAHAYA ◽  
Sirajo Lawan BICHI
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation
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