Exact and Numerical Solution of Abel Integral Equations by Orthonormal Bernoulli Polynomials

2019 ◽  
Vol 5 (6) ◽  
Author(s):  
Mithilesh Singh ◽  
Shivani Singhal ◽  
Nidhi Handa
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Bernoulli Polynomials ◽  
Abel Integral Equations

scholarly journals On Bernstein Polynomials Method to the System of Abel Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Jafarian ◽  
S. Measoomy Nia ◽  
Alireza K. Golmankhaneh ◽  
D. Baleanu
Keyword(s):  
Linear System ◽  
Numerical Solution ◽  
Integral Equations ◽  
Bernstein Polynomials ◽  
Singular System ◽  
Special Kind ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Abel Integral Equations ◽  
The Given

This paper deals with a new implementation of the Bernstein polynomials method to the numerical solution of a special kind of singular system. For this aim, first the truncated Bernstein series polynomials of the solution functions are substituted in the given problem. Using some properties of these polynomials, the solution of the problem is reduced to solve a linear system of algebraic equations. In order to confirm the reliability and accuracy of the proposed method, some weakly Abel integral equations systems with comparisons are solved in detail as numerical examples.

scholarly journals Numerical solution of the integral equations of the electromagnetic field in geosteering problems

2021 ◽  
Vol 1715 ◽  
pp. 012028
Author(s):  
A.V. Bondarenko ◽  
N. N. Velker ◽  
D.Yu. Kushnir ◽  
G.V. Dyatlov ◽  
Yu.A. Dashevsky
Keyword(s):  
Electromagnetic Field ◽  
Numerical Solution ◽  
Integral Equations
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