An approximate solution of nonlinear hypersingular integral equations

2014 ◽  
Vol 86 ◽  
pp. 1-21 ◽  
Author(s):  
I.V. Boykov ◽  
E.S. Ventsel ◽  
V.A. Roudnev ◽  
A.I. Boykova
Keyword(s):  
Approximate Solution ◽  
Integral Equations ◽  
Hypersingular Integral ◽  
Hypersingular Integral Equations

scholarly journals Approximate Solution and its Convergence Analysis for Hypersingular Integral Equations

2019 ◽  
Vol 69 (2) ◽  
pp. 173-178
Author(s):  
Vaishali Sharma ◽  
Amit Setia
Keyword(s):  
Approximate Solution ◽  
Integral Equations ◽  
Analytic Solution ◽  
Singular Integral Equations ◽  
Approximate Solutions ◽  
Algebraic Equations ◽  
Hypersingular Integral ◽  
Hypersingular Integral Equations ◽  
Flight Vehicles ◽  
Theoretical Results

This paper propose a residual based Galerkin method with Legendre polynomial as a basis functions to find the approximate solution of hypersingular integral equations. These equations   occur quite naturally in the field of aeronautics  such as  problem of aerodynamics of flight vehicles  and during mathematical modeling  of  vortex  wakes  behind  aircraft.  The analytic solution of these kind of equations is known only for a particular case ( m(x,t) =0 in Eqn (1)).  Also,   in these  singular integral equations which occur during the formulation of many boundary value problems, the known function  m(x,t) in (Eqn (1)) is not always   zero.  Our proposed method find the approximate solution by converting the integral equations into a linear system of algebraic equations which is easy to solve. The convergence of sequence of approximate solutions is proved and error bound is obtained theoretically. The validation of derived theoretical results and implementation of method is also shown with the aid of numerical illustrations.                            

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