Approximate solutions of linear Volterra integral equation systems with variable coefficients

Applied Mathematical Modelling

Volumn 34, Issue 11, 2010, Pages 3451-3464

  Sorkun, Hüseyin Hilmi ^a   Yalçinbaş, Salih ^a  

^a CELAL BAYAR UNIVERSITY   (Turkey)

Author keywords

System of integral equations; Taylor polynomials; Taylor series; Volterra integral equations

Indexed keywords

ANALYTIC SOLUTION; APPROXIMATE METHODS; APPROXIMATE SOLUTION; EXACT SOLUTION; INTEGRAL SYSTEMS; LINEAR VOLTERRA INTEGRAL EQUATION; MATRIX EQUATIONS; NEW SYSTEM; SYSTEM OF INTEGRAL EQUATIONS; SYSTEM OF LINEAR ALGEBRAIC EQUATIONS; TAYLOR COEFFICIENTS; TAYLOR POLYNOMIALS; VARIABLE COEFFICIENTS; VOLTERRA INTEGRAL EQUATIONS;

APPROXIMATION THEORY; POLYNOMIALS; TAYLOR SERIES;

INTEGRAL EQUATIONS;

EID: 77952954172     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2010.02.034     Document Type: Article

References (29)

1. Baker C.T.H. A perspective on the numerical treatment of Volterra equations. J. Comput. Appl. Math. 2000, 125:217-249.
2. Linz P. Analytical and Numerical Methods for Volterra Equations 1985, SIAM, Philadelphia, PA.
3. Burton T.A. Volterra Integral and Differential Equations 2005, Elsevier B.V., Netherlands.
4. Brunner H. Collocation Method for Volterra Integral and Related Functional Equations 2004, Cambridge University Press, Cambridge.
5. Maleknejad K., Aghazadeh N. Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method. Appl. Math. Comput. 2005, 161:915-922.
6. Delves L.M., Mohamed J.L. Computational Methods for Integral Equations 1985, Cambridge University Press, Cambridge.
7. Maleknejad K., Kajani M.T., Mahmoudi Y. Numerical solution of Fredholm and Volterra integral equation of the second kind by using Legendre wavelets. Kybernetes 2003, 32(9-10):1530-1539.
8. Sezer M. Taylor polynomial solution of Volterra integral equations. Int. J. Math. Edu. Sci. Tech. 1994, 25(5):625.
9. Yalçi{dotless}nbaş S. Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations. Appl. Math. Comput. 2002, 127:195-206.
10. Maleknejad K., Sohrabi S., Rostami Y. Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials. Appl. Math. Comput. 2007, 188:123-128.
11. Akyüz-Daşçi{dotless}oĝlu A., Sezer M. Chebyshev polynomial solutions of systems of higher-order linear Fredholh-Volterra integro-differential equations. J. Franklin Inst. 2005, 342:688-701.
12. Ghasemi M., Tavassoli Kajani M., Bobolian E. Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method. Appl. Math. Comput. 2007, 188:446-449.
13. Biazar J., Ghazvini H. He's homotopy perturbation method for solving system of Volterra integral equations of the second kind. Chaos Solitons Fract. 2009, 39(2):770-777.
14. Tahmasbi A., Fard O.S. Numerical solution of linear Volterra integral equations system of the second kind. Appl. Math. Comput. 2008, 201:547-552.
15. Rabbani M., Maleknejad K., Aghazadeh N. Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method. Appl. Math. Comput. 2007, 187:1143-1146.
16. Abdou M.A. Fredholm-Volterra integral equation of the first kind and contact problem. Appl. Math. Comput. 2002, 125:177-193.
17. Holmaker K. Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones. SIAM J. Math. Anal. 1993, 24(1):116-128.
18. Forbes L.K., Crozier S., Doddrell D.M. Calculating current densities and fields produced by shielded magnetic resonance imaging probes. SIAM J. Appl. Math. 1997, 57(2):401-425.
19. van der Houwen P.J., Sommeijer B.P. Euler-Chebyshev methods for integro-differential equations. Appl. Numer. Math. 1997, 24:203-218.
20. Enright W.H., Hu M. Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay. Appl. Numer. Math. 1997, 24:175-190.
21. Maleknejad K., Mirzae F., Abbasbandy S. Solving linear integro-differential equations system by using rationalized Haar functions method. Appl. Math. Comput. 2004, 155:317-328.
22. Maleknejad K., Tavassoli Kajani M. Solving linear integro-differential equation system by Galerkin methods with hybrid functions. Appl. Math. Comput. 2004, 159:603-612.
23. Kanwall R.P., Liu K.C. A Taylor expansion approach for solving integral equations. Int. J. Math. Ed. Sci. Technol. 1989, 20(3):411-414.
24. Sezer M. A method for the approximate solution of the second-order linear differential equations in terms of Taylor polynomials. Int. J. Math. Ed. Sci. Technol. 1996, 27(6):821-834.
25. Yalçi{dotless}nbaş S., Sezer M. The approximate solution of high-order linear Volterra Fredholm integro-differential equations in terms of Taylor polynomials. Appl. Math. Comput. 2000, 112:291-308.
26. S. Yalçi{dotless}nbaş, A. Şahiner, M. Demirbaş, B. Alti{dotless}nay, S. Kocakuş, The approximate solution of high-order linear differential equation systems with variable coefficients in terms of Taylor polynomials, in: The Third International Conference " Tools for mathematical modelling" , Saint Petersburg, vol. 8, 18-23 June 2001, pp. 175-188.
27. Yalçi{dotless}nbaş S., Yeniçerioĝlu F. The approximate solutions of high-order linear differential equation systems with variable coefficients. Far East J. Dyn. Syst. 2004, 6(2):139-157.
28. Yalçinbaş S., Sezer M., Hilmi Sorkun H. Legendre polynomial solutions of high-order linear Fredholm integro-differential equations. Appl. Math. Comput. 2009, 210(2):334-349.
29. A. Bildik N., Konuralp, S. Yalçi{dotless}nbaş, Comparison of Legendre polynomial approximation and variational iteration method for the solutions of general linear Fredholm integro-differential equations, Comput. Math. Appl., in press.