Galerkin Approximations for the Solution of Fredholm Volterra Integral Equation of Second Kind

Authors

  • Asma Akter Akhia Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
  • Goutam Saha Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh

DOI:

https://doi.org/10.3329/ganit.v41i1.55022

Keywords:

Fredholm Volterra Integral Equation; BF, CH, CL, FL and LLE polynomials; Galerkin Method

Abstract

In this research, we have introduced Galerkin method for finding approximate solutions of Fredholm Volterra Integral Equation (FVIE) of 2nd kind, and this method shows the result in respect of the linear combinations of basis polynomials. Here, BF (product of Bernstein and Fibonacci polynomials), CH (product of Chebyshev and Hermite polynomials), CL (product of Chebyshev and Laguerre polynomials), FL (product of Fibonacci and Laguerre polynomials) and LLE (product of Legendre and Laguerre polynomials) polynomials are established and considered as basis function in Galerkin method. Also, we have tried to observe the behavior of all these approximate solutions finding from Galerkin method for different problems and then a comparison is shown using some standard error estimations. In addition, we observe the error graphs of numerical solutions in Galerkin method for different problems of FVIE of second kind.

GANITJ. Bangladesh Math. Soc.41.1 (2021) 1–14

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Published

2021-10-05

How to Cite

Akhia, A. A. ., & Saha, G. . (2021). Galerkin Approximations for the Solution of Fredholm Volterra Integral Equation of Second Kind. GANIT: Journal of Bangladesh Mathematical Society, 41(1), 1–14. https://doi.org/10.3329/ganit.v41i1.55022

Issue

Vol. 41 No. 1 (2021)

Section

Articles

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The copyright of GANIT: Journal of Bangladesh Mathematical Society is reserved by Bangladesh Mathematical Society (web: https://bdmathsociety.org/)