A new collocation method for solution of mixed linear Integro-differential difference equations

Abstract

The aim of this article is to present an efficient numerical procedure for solving mixed linear integro-differential-differenceequations. Our method depends mainly on a Taylor expansion approach. This method transforms mixed linear integro-differentialdifference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. Thereliability and effiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computerprogram in Maple10

Keywords

• Mixed linear integro-differential-difference equations,Taylor polynomials and series; collocation points

Kaynakça

1. S. Yalc¸ınbas¸, Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput. 127 (2002)196- 20
2. M. G¨ulsu, M. Sezer, On the solution of the Riccati equation by the Taylor matrix method, Appl. Math. Comput. 188 (2007) 446-4
3. M. Sezer, Taylor polynomial solution of Volterra integral equations, Int. J. Math. Educ. Sci. Technol. 25 (5) (1994) 625-633.
4. M. Sezer, M. G¨ulsu, A new polynomial approach for solving difference and Fredholm integro-difference equations with mixed argument, Appl. Math. Comput. 171 (2005) 332-344.
5. S. Yalc¸ınbas¸, M. Sezer, The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials, Appl. Math. Comput. 112 (2000) 291-308.
6. M. Sezer, A method for approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J. Math. Educ. Sci. Technol. 27 (6) (1996) 821-834.
7. S¸. Nas, S. Yalc¸ınbas¸, M. Sezer, A method for approximate solution of the high-order linear Fredholm integro-differential equations, Int. J. Math. Educ. Sci. Technol. 27 (6) (1996) 821-834.
8. A. Karamete, M. Sezer, A Taylor collocation method for the solution of linear integro-differential equations, Int. J. Comput. Math. 79 (9) (2002) 987-1000.

9. M. G¨ulsu, M. Sezer, A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Int. J. Comput. Math 82 (5) (2005) 629-642.
10. B. B¨ulb¨ul, M. G¨ulsu, M. Sezer, A new Taylor collocation method for nonlinear Fredholm-Volterra integro-differential equations, Numer. Methods Partial Diff. Eq. doi 10.1002/num.20470.
11. T. L. Saaty Modern Nonlinear Equations, Dover Publications Inc., New York, 1981.
12. F. Karakoc¸, H. Bereketo˘glu, Solutions of delay differential equations by using differential Transform method, Int. J. Comput. Math. 86 (2009) 914-923.
13. M. Sezer, S. Yalc¸ınbas¸, N. S¸ahin, Approximate solution of multi-pantograph equation with variable coefficients, J. Comput. Appl. Math. 214 (2008) 406-416.
14. B. G¨urb¨uz, M. G¨ulsu, M. Sezer, Numerical approach of high-order linear delay difference equations with variable coefficients in terms of Laguerre polynomials, Math. Comput. Appl., 16 (2011) 267-278.
15. B. G¨urb¨uz, M. Sezer, Laguerre collocation method for solving Fredholm integro-differential equations with functional arguments, J. Appl. Math. 2014 (2014) 12.