# Solving of Nonlinear System of Fredholm-volterra Integro-differential Equations by Using Discrete Collocation Method

Volume 3, Issue 4, pp 382--389
• 1181 Views ### Authors

M. Rabbani - Department of mathematics, Sari Branch, Islamic Azad University, Sari, Iran S. H. Kiasoltani - Department of mathematics, Noshahar Branch, Islamic Azad university, Noshahar, Iran

### Abstract

In this paper, we solve nonlinear system of Fredholm-Volterra integro-differential equations by using discrete collocation method. These types of systems of integral equations are important and they can be used in engineering and some of the applied sciences such as population dynamics, reaction-diffusion in small cells and models of epidemic diffusion. Also these equations with convolution kernel can be solved by discrete collocation method. By the above mentioned method we approximate solution of equation by no smooth piecewise polynomials, for validity and ability the method we solve some examples with high accuracy.

### Keywords

• Fredholm-Volterra integro-differential equations
• discrete collocation method

•  65R20
•  45J05
•  45G10
•  65H10

### References

•  K. E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge (1997)

•  A. Ayad, Spline approximation for first order Fredholm integro-differential equations, Studia Univ. Babes-Bolyai Math., 41 (1996), 1--8

•  H. Brunner, Collocation Method for Volterra Integral and Related Functional Equations, Cambridge University Press, Combridge (2004)

•  M. Lakestani, M. Razzaghi, M. Dehghan, Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations, Math. Probl. Eng., 2006 (2006), 12 pages

•  C. Lubich, Convolution Quadrature and Discretized Operational Calculus II, Numerische Mathematik, 52 (1988), 413--425

•  K. Maleknejad, M. Karami, Using the WPG method for Solving Integral equations of the second kind, Appl. Math. Comput., 166 (2005), 123--130

•  M. Rabbani, K. Maleknejad, N. Aghazadeh, Numerical computational solution of the volterra integral system of the second kind by using an expansion method, Applied Mathematics and Computation, 187 (2007), 1143--1146

•  K. Maleknejad, M. Rabbani, N. Aghazadeh, M. Karami, A wavelet Petrov–Galerkin method for solving integro-differential equations, International Journal of Computer Mathematics, 86 (2009), 1572--1590