**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31100

##### Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials

**Authors:**
N. M. A. Nik Long,
Z. K. Eshkuvatov,
M. Yaghobifar,
M. Hasan

**Abstract:**

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

**Keywords:**
Approximation,
Galerkin Method,
Integral
equations,
Laguerre polynomial

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1327732

**References:**

[1] A.Akyuz-Dasc─▒oglu (2004). Chebyshev polynomial solutions of systems of linear integral equations. Applied Mathematics and Computation, 151, pp. 221-232.

[2] K.E. Atkinson. The numerical of integral equation of the second kind, Cambridge press, 1997.

[3] E. Babolian and F. Fattahzadeh (2007). Numerical computation method in solving integral equations by using Chebyshev wavelet operational matrix of integration. Applied Mathematics and Computation 188, pp. 1016-1022.

[4] D. Elliott (1963). A Chebyshev series method for the numerical solution of Fredholm integral equation, Comp.J, 6, pp. 102-111.

[5] F.D. Gakhov. Boundary Value Problems. Pergamon Press.1966.

[6] L. Kantorovich (1948) Functional analysis and applied mathematics, Uspehi Mat. Nauk, 3, pp. 89-185.

[7] L. Kantorovich and G. Akilov. Function analysis in Normed spaces. Pergamon, Press Oxford. 1982.

[8] K. Maleknejad, S. Sohrabi, Y. Rostami (2007). Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials. Applied Mathematics and Computation 188, pp.123-128.

[9] K. Maleknejad, T. Lotfi (2005). Numerical expansion methods for solving integral equations by interpolation and Gauss quadrature rules. Applied Mathematics and Computation 168, pp. 111-124.

[10] N.I Muskhelishvili. Singular integral equations. Noordhoff, Holland, 1953.

[11] A. Palamara Orsi (1996). Product integration for Volterra integral equations of the second kind with weakly singular kernels, Math. Comp. 65, pp. 1201-1212.

[12] A.D. Polyanin and A. V. Manzhirov. Handbook of integral equations. Boca Raton, Fla.: CRC Press, 1998.

[13] D. Pylak, R. Smarzewski, M. A. Sheshko (2005). Differential Equation, Vol. 41, No. 12, pp. 1775-1788.

[14] D.G. Sanikidze (2005). On the numerical solution of a class of singular integral equations on an infinite interval. Differential Equations, Vol. 41, No 9, pp. 1353-1358.