Document Type : Research Paper

Author

• Bahman Babayar-Razlighi

Department of Mathematics, Faculty of science, Qom University of Technology, Qom, Iran

Abstract

In this paper, we develop and apply the extrapolation method to a large class of nonlinear systems of Volterra integral equations. These systems arise in many physical and medical phenomena models, such as plasma and diseases, which can be investigated through mathematical models. The solutions of such systems require to be obtained on a long independent variable interval. We show that for such kernels, this method converges on a long interval. We apply the method on the unit interval $[0,1]$ and obtain the solution through $[0,1]$. Then, we apply the method on $[1,2]$, and use the solution on $[0,1]$ as the lag term; hence, we obtain the solution on $[0,2]$. We continue this procedure on $[0,n]$, for some positive integer $n$. We show that in the presented kernel, the error on $[0,n]$ is not propagated to $[n,n+1]$. Hence, we can use the proposed method on a long interval and also for stiff problems. We give a total algorithm for the proposed method and then establish a convergence analysis for it. As we shall see in the last example, the method is a powerful technique for stiff problems. Finally, we show the applicability and accuracy of the method in some sample problems.

Keywords

• Extrapolation method
• Nonlinear Volterra integral system
• Stiff problems
• Lag terms
• Long interval