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BERNSTEIN’S APPROXIMATION OF GENERALIZED ABEL’S INTEGRAL EQUATION WITH APPLICATION IN TOMOGRAPHY

Shiva Sharma, Prashant K. Pandey, Rajesh K. Pandey, Kamlesh Kumar

Abstract


This paper presents the Bernstein and hybrid Bernstein approximations to solve the generalized Abel’s integral equations (GAIEs) via collocation approach. Bernstein polynomial and hybrid Bernstein functions are used in the approximation of GAIEs solutions and convergence analysis are presented in detail. To show the validity of the proposed methods, numerical examples are considered and an application is shown through Abel inversion in tomography.

Keywords


Abel’s equation; Bernstein polynomial; Block-Pulse function; Collocation method; Hybrid Bernstein Block- Pulse function

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References


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DOI: http://dx.doi.org/10.6084/ijact.v8i2.863

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