Burcu Gürbüz, Mehmet Sezer
986 290


In this paper, a numerical algorithm based on Laguerre and Taylor
polynomials is applied for solving a class of functional integrodi
erential equations. The considered problem is transfered to a matrix
equation which corresponds to a system of linear algebraic equations
by Hybrid collocation method under the mixed conditions. The
reliability and eciency of the proposed scheme are demonstrated by
some numerical experiments. Also, the approximate solutions are corrected by using the residual correction.


Linear functional-differential equations; Taylor and Laguerre polynomials and series; Algorithms for functional approximation; Collocation methods

Full Text:



J. Dieudonne, Orthogonal polynomials and applications, Berlin, New York, 1985.

S. Chandrasekhar. Introduction to the Study of Stellar Structure. Dover, New York, 1967.

J. Rashidinia, A. Tahmasebi, S. Rahmany, A reliable treatment for nonlinear Volterra integro-differential, J. Inf. Comput. Sci., 9(1) (2014) 003-010.

Z. Chen, X. Cheng, An ecient algorithm for solving Fredholm integro-differential equations with weakly singular kernels, J. Comput. Appl. Math.


J G. Pipe, N. R. Zwart,Spiral Trajectory Design: A Flexible Numerical Algorithm and Base Analytical Equations, Magn. Res. Med., 71 (2014) 278-285.

R. Farnoosh, M. Ebrahimi, Monte Carlo method for solving Fredholm integral

equations, Appl. Math. Comput. 195(1) (2008) 309-315.

A.Ghosh, R. Elber H. A. Scheraga, An atomically detailed study of the folding pathways of protein A with the stochastic difference equation, Nat. Academy Sci., 99 (16) (2002) 10394-10398.

K. Wang, Q. Wang, Taylor collocation method and convergence analysis

for the Volterra-Fredholm integral equations, J. Comput. Appl. Math. (2014)

A. Ovchinnikov, Dierence integrability conditions for parameterized linear difference and differential equations, Adv. Appl. Math. 53 (2004) 61-71.

G.A Andrews, R. Askey, Roy R., Special Functions, Cambridge, 2000.

P.K. Sahu, S. Saha Ray, Numerical solutions for the system of Fredholm

integral equations of second kind by a new approach involving semiorthogonal B-spline wavelet collocation method, Appl. Math. Comput., 2014.

S. Sedaghata, Y. Ordokhania, M. Dehghanb, On spectral method for Volterra functional integro-differential equations of neutral type, Numer. Func. Anal.

Opt., 35 (2014) 223-239.

S. Mashayekhi, M. Razzaghi, O. Tripak, Solution of the nonlinear mixed Volterra-Fredholm integral equations by hybrid of blockpulse functions and Bernoulli polynomials, The Sci. World J.,,2014.

M. Gulsu, Y. Ozturk, M. Sezer, Numerical approach for solving Volterra

integro-differential equations with piecewise intervals, J. Avdan. Research

Appl. Math. 4(1) (2012) 23-37.

M. Gulsu, Y. Ozturk, Numerical approach for the solution of hypersingular

integro-differential equations, Appl. Math. Comp. 230 (2014) 701-710.

S. Bayn, Mathematical Methods in Science and Engineering, New Jersey,

John Willey & Sons, 2006.

B. Gurbuz, M. Gulsu, M. Sezer, Numerical approach of high-order linear delay

dierence equations with variable coefficients in terms of Laguerre polynomials,

Math. Comput. Appl. , 16 (1)(2011) 267-278.

S. Yuzbas, N. Sahin, A numerical approach for solving linear dierential

equation systems,Journ. Adv. Res. Sci. Comput. 3(3) (2011) 14-29.

B. Gurbuz, M. Sezer, Coskun Guler, Laguerre Collocation Method for Solving

Fredholm Integro-Differential Equations with Functional Arguments, (2014)

ID:682398, 12.

A. Akyuz Dascioglu, H. Cerdik Yaslan, The solution of high-order nonlinear

differential equations by Chebyshev Series, Appl. Math. Comput. 217 (2011)


S. Yuzbas, E. Gok, M. Sezer, Muntz-Legendre polynomial solutions of linear

delay fredholm integro-dierential equations and residual correction, Math.

Comput. Appl. 18(3) (2013) 476-485.

S. Yuzbas, M. Sezer, An improved Bessel collocation method with a residual

error function to solve a class of Lane-Emden differential equations, Math.

Comput. Model. 57(5-6) (2013) 1298-1311.

M. Turkylmaz, An eective approach for numerical solutions of highorder

Fredholm integro-dierential equations, Appl. Math. Comput., (2014)

S. Yuzbas, A Bessel Polynomial Approach For Solving General Linear Fredholm

Integro-Differential- Difference Equations", Int. Journ. Comput. Math.

(2011) 3093-3111.

S. Yuzbas, Laguerre approach for solving pantograph-type Volterra integro-differential equations, Appl. Math. Comput. 232 (2014) 1183-1199.

M. Sezer, M. Gulsu, A new polynomial approach for solving dierence and

Fredholm integro-difference equations with mixed argument, Appl. Math.

Compt. 171 (2005) 332-344.

M. Gulsu, Y. Ozturk, A new collocation method for solution of mixed linear

integro-differential equations, Appl. Math. Comput. 216 (2010) 2183-2198.

K. Wang, Q.Wang, Taylor collocation method and convergence analysis for

the Volterra-Fredholm integral equations, Journ. Comput. Appl. Math. 260

(2014) 294-300.

E. H. Doha, D. Baleanu, A. H. Bhrawy, M. A. Abdelkawy, A Jacobi collocation

method for solving nonlinear burgers-type equations, Hindawi, ID 760542:12,


S. Alavi, A. Heydari, An Analytic approximate solution of the matrix Riccati

differential equation arising from the LQ optimal control problems, Journ.

Adv. Math. 5(3) (2014) 731-738.

J. P. Dahm, A. Arbor, K. Fidkowski, Error estimation and adaptation

in hybridized discontinous Galerkin methods, The AIAA, (2014)