Numerical solution of random love's integral equation

An analytical solution to applied mathematics-related Love’s equation using the Boubaker polynomials expansion scheme

“…2, that the mean deviation between the proposed solution and that of Piessens et al [34] does not exceed 7%. The behavior of the solution, for increasing values of k is in good agreement with the results of Boland [35], Fox et al [15,36], Sambandham et al [7] and Christenscn et al [8]. The proposed solution yields values which seem to decrease toward unity with increasing values of k. This feature can be explained both mathematically and experimentally.…”

“…Among the most cited, one can evoke the studies of Shimasaki et al [1], Theocaris [2], Golberg [3], Scarton [4], Erdogan et al [5], Sambandham [6][7][8] …”

“…In the last four decades, Fredholm-type differential equations [1][2][3][4][5][6][7][8][9][10] have shown a big interest in the domains of aerodynamics, fracture mechanics hydrodynamics and polymer physics; there has been a great deal of interest in the numerical solutions of integral equations of Cauchy type, Kirkwood-Riseman type, etc., which have considerable application in mathematical physics and engineering. In view of the wide applicability of integral equations, it is necessary to develop numerical techniques to solve them.…”

A Novel Approach for the Solution of a Love’s Integral Equations Using Bernstein Polynomials

“…For literature related to the numerical solutions of singular integral equations of the deterministic type, a surveys of different analytical methods for the solution of random integral equations has been proposed by Bharucha-Reid [5] and Christensen et al [6]. Love's equations were early established by Love [10][11][12][15][16][17][18] for solving some magnetic and electrical fields problems. The actual study is concerned with calculation of the normalized field created conjointly by two similar plates of radius R, separated by a distance , where is a positive real parameter, and at equal or opposite potential, with zero potential at infinity, is the solution of the Love's [16][17] second kind integral equation:…”

“…Considering that many real-world mathematical problems, especially in the area of applied mathematics are too complicated to be solved in exact terms, the using of numerical methods has been swiftly developed recently. Love's integral equation (Fredholm equation of the second kind) [5][6][7][8][9][10][11][12][13][14] has shown a big interest in the several applied physics fields such as polymer structures, aerodynamics, fracture mechanics hydrodynamics and elasticity engineering. For literature related to the numerical solutions of singular integral equations of the deterministic type, a surveys of different analytical methods for the solution of random integral equations has been proposed by Bharucha-Reid [5] and Christensen et al [6].…”