Convergence of approximate solution of delay Volterra integral equations

Document Type : Research Article

Authors

• M. Zarebnia
• L. Shiri

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.

10.22067/ijnao.v6i2.47972

Abstract

In this paper, sinc-collocation method is discussed to solve Volterra func tional integral equations with delay function (t). Also the existence and uniqueness of numerical solutions for these equations are provided. This method improves conventional results and achieves exponential convergence. Numerical results are included to confirm the efficiency and accuracy of the method.

Keywords

• Volterra functional integral equations
• delay function
• sinc- collocation

20.1001.1.24236977.2016.6.2.3.7

---

References

1. Brunner, H. Iterated collocation methods for Volterra integral equations with delay arguments, Math. Comput. 62 (1994), 581-599.

2. Brunner, H., Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge 2004.

3. Denisov, A.M. and Lorenzi, A. Existence results and regularisation techniques for severely ill-posed integrofunctional equations, Boll. Un. Mat. Ital. 11 (1997), 713-731.

4. Iserles, A. On the generalized pantograph functional differential equation, European J. Appl. Math. 4 (1993), 1-38.

5. Li, Y.K. and Kuang, Y. Periodic solutions of periodic delay Lotka-Volterra equations and systems, J. Math. Anal. Appl. 255 (2001), 260-280.

6. Linz, P. and Wang, R.L.C. Error bounds for the solution of Volterra and delay equations, Appl. Numer. Math. 9 (1992), 201207.

7. Okayama, T., Matsuo, T. and Sugihara, M. Error estimates with explicit constants for Sinc approximation, Sinc quadrature and Sinc inde_nite integration, Mathematical Engineering Technical Reports 2009-01, The University of Tokyo, 2009.

8. Stenger, F. Handbook of Sinc Numerical Methods, Springer, New York 2011.

9. Stenger, F. Numerical Methods Based on Sinc and Analytic Functions, Springer, New York 1993.

10. Xie, H.H., Zhang, R. and Brunner, H. Collocation Methods for General Volterra Functional Integral Equations with Vanishing Delays, SIAM J. Sci. Comp. 33 (2011), 3303-3332.

11. Zarebnia, M. and Rashidinia, J. Convergence of the Sinc method applied to Volterra integral equations, Appl. Appl. Math, 5 (2010), 198-216.