Analytical Solution of the Integral Equations for the Current by the Averaging Method

2008 ◽  
pp. 1-10
Author(s):  
Mikhail V. Nesterenko ◽  
Victor A. Katrich ◽  
Yuriy M. Penkin ◽  
Sergey L. Berdnik
Keyword(s):  
Analytical Solution ◽  
Integral Equations ◽  
Averaging Method

scholarly journals Analytical Solution of System of Volterra Integral Equations Using OHAM

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muhammad Akbar ◽  
Rashid Nawaz ◽  
Sumbal Ahsan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Numerical Methods ◽  
Analytical Solution ◽  
Integral Equations ◽  
Function Method ◽  
Auxiliary Function ◽  
Volterra Integral Equations ◽  
Large Parameter ◽  
Reliable Technique ◽  
Present Technique ◽  
Optimal Homotopy Asymptotic Method

In this work, a reliable technique is used for the solution of a system of Volterra integral equations (VIEs), called optimal homotopy asymptotic method (OHAM). The proposed technique is successfully applied for the solution of different problems, and comparison is made with the relaxed Monto Carlo method (RMCM) and hat basis function method (HBFM). The comparisons show that the present technique is more suitable and reliable for the solution of a system of VIEs. The presented technique uses auxiliary function containing auxiliary constants, which control the convergence. Moreover, OHAM does not require discretization like other numerical methods and is also free from small or large parameter.

scholarly journals Analytical Solution for Differential and Nonlinear Integral Equations via F ϖ e -Suzuki Contractions in Modified ϖ e -Metric-Like Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Analytical Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Nonlinear Integral Equations ◽  
New Space

The aim of this manuscript is to present a new space, namely, a modified ϖ e -metric-like space, and we establish some related fixed point results using extended F ϖ e -Suzuki and generalized F ϖ e -Suzuki contractions on the mentioned space. Here, we support our theoretical consequences in two ways: the first one consists of presenting illustrative examples and the second one consists of finding analytical solutions for some integral and differential equations in the context of the mentioned space.

On Maxwell's equations in non-stationary media

2008 ◽  
Vol 366 (1871) ◽  
pp. 1781-1788 ◽  
Author(s):  
I Vorgul
Keyword(s):  
Analytical Solution ◽  
Plane Wave ◽  
Integral Equations ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Exact Analytical Solution ◽  
Charge Injection ◽  
Incident Field ◽  
Volterra Integral Equations ◽  
Numerical Investigations

Maxwell's equations formulated for media with gradually changing conductivity are reduced to Volterra integral equations. Analytical and numerical investigations of the equations are presented for the case of gradual splash-like change in conductivity. Splash-like change in medium parameters can model any discharge phenomena, growing plasma, charge injection, etc. Exact analytical solution for the resolvent is presented and different field behaviours are analysed for the incident field as a plane wave and as an impulse.

scholarly journals A new analytical solution procedure for nonlinear integral equations

2012 ◽  
Vol 55 (7-8) ◽  
pp. 1892-1897 ◽  
Author(s):  
Majid Khan ◽  
Muhammad Asif Gondal ◽  
Sunil Kumar
Keyword(s):  
Analytical Solution ◽  
Integral Equations ◽  
Solution Procedure ◽  
Nonlinear Integral Equations

scholarly journals INVESTIGATION OF THE BOUNDARY-VALUED PROBLEM ON RESONANCE MHD NON-UNIFORMITY BY INTEGRAL EQUATIONS USING

2021 ◽  
pp. 90-95
Author(s):  
Y.N. Oleksandrov ◽  
I.Sh. Nevliudov ◽  
O.O. Chala ◽  
I.B. Botsman ◽  
V.V. Nevliudova
Keyword(s):  
Numerical Simulation ◽  
Analytical Solution ◽  
Integral Equations ◽  
Method Of Integral Equations ◽  
Field Velocity

Numerical simulation of interior field velocity is studied on the basis of the rigorous analytical solution of the boundary-valued magnetohydrodynamics problem on the sphere type non-uniformities. The basis for the analytical solution is the method of integral equations of linear magnetohydrodynamics. The analysis of the obtained results is carried out.

scholarly journals Analytical Solution of Urysohn Integral Equations by Fixed Point Technique in Complex Valued Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 852 ◽  
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Analytical Solution ◽  
Unique Solution ◽  
Integral Equations ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Fixed Point Result ◽  
Urysohn Integral Equations ◽  
Fixed Point Technique ◽  
Complex Valued

The purpose of this article is to introduce a fixed point result for a general contractive condition in the context of complex valued metric spaces. Also, some important corollaries under this contractive condition are obtained. As an application, we find a unique solution for Urysohn integral equations, and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. Previous known related results in the literarure and some other known results in the literature.

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