IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF COMPUTER SCIENCE AND MATHEMATICAL THEORY (IJCSMT )

E-ISSN 2545-5699
P-ISSN 2695-1924
VOL. 8 NO. 2 2022
DOI: https://doi.org/10.56201/ijcsmt.v8.no2.2022.pg50.55

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The Numerical Solution of Volterra Integral Equations of the First Kind Using Hermite Polynomials via the Galerkin’s Residual Method

Kamoh, N. M., Ali, H. and Dang, B. C

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Abstract

In this paper, the method for solving Volterra integral equations of the first kind with weakly singular kernels using the Hermite polynomials is presented. The procedure resulted in the construction of systems of algebraic equations, solving these systems of algebraic equations an approximate solution ?( ) is obtained numerically; Illustrative examples are included to demonstrate the simplicity and applicability of the method. Once the approximate solution coincides with the exact solution for any particular value of , further evaluations can only give an approximate solution. The volume of work involve in this method is much easier than most of the existing methods contained in the literature.

keywords:

Galerkin’s method, Hermite polynomials, kernels, Volterra integral equations, kernels.

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References:

J. E. Cicelia, (2014): Solution of Weighted Residual Problems by using Galerkin’s
Method, Indian Journal of Science and Technology, 7(3S), 52–54.

Rahman, M. A., Islam, M. S., and Alam, M. M., (2012): Numerical Solutions of Volterra
Integral Equations Using Laguerre Polynomials. Journal of Scientific research, 4 (2),
357-364

A. Altürk (2016): Application of the Bernstein Polynomials for Solving Volterra Integral
Equations with Convolution Kernels, Filomat, 30(4): 1045-1052, DOI:
10.2298/FIL1604045A
A. Bellour and E. A. Rawashdeh (2010): Numerical Solution of First Kind Integral
equations by Using Taylor Polynomials, Journal of Inequalities and Special Functions,
1(2), 23-29.

K. Wang and Q. Wang (2014): Taylor polynomial method and error estimation for a kind
of mixed Volterra-Fredholm integral equations, Applied Mathematics and Computation,
vol. 229, No. C
Reinkenhof, J., (1977): Differentiation and integration using Bernstein’s polynomials,
International Journal of Numerical Methods and Engineering, 11, 1627 – 1630.
Kreyszig, E., (1979): Bernstein polynomials and numerical integration, International
Journal of Numerical Methods and Engineering, 14, 292 – 295.

Mandal, B. N., Bhattacharya, S., (2007): Numerical solution of some classes of integral
equations using Bernstein polynomials, Applied Mathematics and Computation, 190,
1707 – 1716.

Subhra Bhattacharya and Mandal, B.N., (2008): Use of Bernstein Polynomials in
numerical solution of Volterra integral equations Applied Mathematical Sciences, Vol. 2,
36, 1773 – 1787.

Farshid Mirzaee., (2012): Numerical Solution for Volterra Integral Equations of the First
Kind via Quadrature Rule, Applied Mathematical Sciences, Vol. 6, (20), 969 – 974.

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