Numerical Treatment of Mixed Volterra-Fredholm Integral Equations Using Trigonometric Functions and Laguerre Polynomials

Main Article Content

Pakhshan Mohammed Ameen Hasan
Nejmaddin Abdulla Sulaiman


Trigonometric functions, Laguerre polynomials, least square technique, linear algebraic system, linear mixed Volterra-Fredholm integral equation of the second kind (LMV-FIE2nd).




In this paper, numerical solution of linear mixed Volterra-Fredholm integral equations of the second kind by using trigonometric functions and Laguerre polynomials approximation accompanied with the least square technique is presented. For the explanation of the idea and more illustration, an algorithm is introduced, and several examples are solved. Also, comparison between the exact and the approximate solutions are given to show the efficiency of the methods and accuracy of the results

Abstract 11 | PDF Downloads 7


Abdou, M.A. 2002. Integral Equation of Mixed Type
and Integrals of Orthogonal Polynomials. Journal of
Computational and Applied Mathematics. 138(2):

Abdou, M.A. 2002. Fredholm-Volterra Integral Equation
of the First Kind and contact Problem, J. Applied
Mathematics and Computation. 125(2-3): 177-193.

Abdou, M.A.2003. On Asymptotic Method for Fredholm
Volterra Integral Equation of the Second Kind in Co-
ntact problem, Journal of Computational and
Applied Mathematics. 154: 431-446.

Abdou, M.A. and Abd Al-Kader G.M., 2005. Mixed
Type of Fredholm-Volterra Integral Equation. Le
Matematiche. LX: 41-58.

Aghajani, A. , Jalilian, Y. and Sadarangani, K., 2012.
Existence of Solution for Mixed Volterra- Fredholm
Integral Equations. Elecronic Journal of Differential
Equations.137: pp. 1-12.

Ahmed, S.S. 2011. Numerical Solution for Volterra-
Fredholm Integral Equation of the Second Kind by
Using Least squares technique. Iraqi Journal of
Science. 52(4): 504-512.

Aleksandrow, V.M. and E.V. Kovalenko. 1968.
Problems in Mechanic Media with Mixed Boundary
Conditions. Nauka Moscow.

Atkinson, K.E. 1997. Numerical Solution of Integral
Equation of the Second Kind. Cambridge.

Constanda, C., 1995. Integral Equation of the First Kind
in Plane Elasticity. Quartly of Aplied Mathematics. v.
LIII (4): 783-793.

Delves, L. and Walsh, J., 1974. Numerical Solution of
Integral Equations. Oxford.

Ezzati, R. and Najafalizadeh, S., 2012. Numerical Meth-
ods for Solving Linear and Nonlinear Volterra-Fred
holm Integral Equations by Using Cas Wavelets.
World Applied Sciences Journal. 18 (12): 1847-1854.

Kauthen, P.G., 1989. Continuous Time Collocation Met-
hods for Volterra-Fredholm Integral Equation. Numer
Math. 56: 409-424.

Maleknejad, K. and Hadizadeh, M. A. 1999. New Comp-
utational Method for Volterra-Fredholm Integral Equ-
ation, J. Comput. Math. Appl. 37: 37-48.

Mkhitarian, S.M. and M.A. Abdou. 1990. On Different
Methods of Solution of the Integral Equation for the
Planer Contact Problem of Elasticity. Dokl. Acad.
Nauk.Arm. SSR. 89(2): 59-74.

Shehab, S.N., Ali, H.A. and H.M. Yaseen. 2010. Least
Square Method for Solving Integral Equations with
Multiple Time Lags. Eng & Tech Journal. 28(10):

Wang, Q., Wang K., and Chen, S., 2014. Least Square
Approximation Method for the Solution of Volterra-
Fredholm Integral Equations. Journal of Computa-
tional and Applied Mathematics.272:141-147.

Wazwaz, A.M. 2011. Linear and Non-linear Integral
Equations. Springer. Saint Xavier University of
Chicago, USA.