scholarly journals Unbounded solution of characteristic singular integral equation using differential transform method

2014 ◽  
Vol 9 (7) ◽  
pp. 2869-2881 ◽  
Author(s):  
Mohammad Abdulkawi Mahiub
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Numerical Results ◽  
Differential Transform Method ◽  
Cauchy Type ◽  
Unbounded Solution ◽  
Transform Method ◽  
Present Solution ◽  
Differential Transform

In this paper, The differential transform method is extended to solve the Cauchy type singular integral equation of the first kind. Unbounded solution of the Cauchy type singular  Integral equation is discussed. Numerical results are shown to illustrate the efficiency and accuracy of the present solution.

scholarly journals Bounded solution of Cauchy type singular integral equation of the first kind using differential transform method

2018 ◽  
Vol 14 (1) ◽  
pp. 7580-7595
Author(s):  
M. Abdulkawi
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Singular Integrals ◽  
Bounded Solution ◽  
Differential Transform Method ◽  
Cauchy Type ◽  
Transform Method ◽  
Differential Transform

In this paper, an efficient approximate solution for solving the Cauchy type singular integral equation of the first kind is presented. Bounded solution of the Cauchy type singular Integral equation is discussed. Two type of kernel, separable and convolution, are considered. The differential transform method is used in the solution. New theorems for transformation of Cauchy singular integrals are given with proofs. Approximate results areshown to illustrate the efficiency and accuracy of the approximate solution.

scholarly journals Решение электродинамической задачи для микрополосковой излучающей структуры с киральной подложкой

2018 ◽  
Vol 44 (11) ◽  
pp. 80
Author(s):  
М.А. Бузова ◽  
Д.С. Клюев ◽  
М.А. Минкин ◽  
А.М. Нещерет ◽  
Ю.В. Соколова
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Surface Current ◽  
Longitudinal Component ◽  
Cauchy Type ◽  
Surface Current Density ◽  
Electrodynamic Problem ◽  
Type Singularity ◽  
Different Types

AbstractWe present a solution of the electrodynamic problem for a microstrip radiating structure with a substrate of a chiral metamaterial using the singular integral representation of the field, which in turn is reduced to a singular integral equation with the Cauchy-type singularity relative to the longitudinal component of the surface current density. Graphs of the current distribution for different types of substrates and the chirality parameters of a substrate are given.

SH-Waves in a Medium Containing a Disordered Periodic Array of Cracks

1995 ◽  
Vol 62 (2) ◽  
pp. 312-319 ◽  
Author(s):  
Y. Mikata
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Numerical Results ◽  
Crack Spacing ◽  
Periodic Array ◽  
Wave Number ◽  
Sh Wave ◽  
Reflection And Transmission ◽  
Dispersion And Attenuation

Reflection and transmission of an SH-wave by a disordered periodic array of coplanar cracks is investigated, and subsequently its application to the dispersion and attenuation of an SH-wave in a disorderedly cracked medium is also treated. This is a stochastic boundary value problem. The formulation largely follows Mikata and Achenbach (1988b). The problem is formulated for an averaged scattered field, and the governing singular integral equation is derived for a conditionally averaged crack-opening displacement using a quasi-crystalline-like approximation. Unlike our previous study (Mikata and Achenbach, 1988b) where a point scatterer approximation was used for the regular part of the integral kernel, however, no further approximation is introduced. The singular integral equation is solved by an eigenfunction expansion involving Chebyschev polynomials. Numerical results are presented for the averaged reflection and transmission coefficients of zeroth order as a function of the wave number for normal incidence, a completely disordered crack spacing, and various values of the ratio of crack length and average crack spacing. Numerical results are also presented for the dispersion and attenuation of an SH-wave in a disorderedly cracked medium.

scholarly journals Solution of Abel Integral Equation Using Differential Transform Method

2018 ◽  
Vol 14 (1) ◽  
pp. 7521-7532
Author(s):  
Subhabrata Mondal ◽  
B. N. Mandal
Keyword(s):  
Applied Sciences ◽  
Integral Equation ◽  
Fractional Order ◽  
Solid Mechanics ◽  
Differential Transform Method ◽  
Transform Method ◽  
Abel Integral Equation ◽  
Differential Transform ◽  
Abel Integral Equations ◽  
Fractional Differential

The application of fractional differential transform method, developed for differential equations of fractional order, are extended to derive exact analytical solutions of fractional order Abel integral equations. The fractional integrations are described in the Riemann-Liouville sense and fractional derivatives are described in the Caputo sense. Abel integral equation occurs in the mathematical modeling of various problems in physics, astrophysics, solid mechanics and applied sciences. An analytic technique for solving Abel integral equation of first kind by the proposed method is introduced here. Also illustrative examples with exact solutions are considered to show the validity and applicability of the proposed method. Abel integral equation, Differential transform method, Fractional differential transform method.

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