A Numerical Solution of Volterra's Population Growth Model Based on Hybrid Function

International Journal Bioautomation

Majid Tavassoli Kajani¹  Khosrow Maleknejad¹  Saeid Jahangiri² 

[1] ;Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran;

关键词: Integro-differential equation;    Chebyshev polynomials;    Block-pulse functions;    Gauss-Chebyshev points;    Hybrid function;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this paper, a new numerical method for solving Volterra's population growth model is presented. Volterra's population growth model is a nonlinear integro-differential equation. In this method, by introducing the combination of fourth kind of Chebyshev polynomials and Block-pulse functions, approximate solution is presented. To do this, at first the interval of equation is divided into small sub-intervals, then approximate solution is obtained for each sub-interval. In each sub-interval, approximate solution is assumed based on introduced combination function with unknown coefficients. In order to calculate unknown coefficients, we imply collocation method with Gauss-Chebyshev points. Finally, the solution of equation is obtained as the sum of solutions at all sub-intervals. Also, it has been shown that upper bound error of approximate solution is O(m^-r/N^0.5). It means that by increasing m and N, error will decrease. At the end, the comparison of numerical results with some existing ones, shows high accuracy of this method.

【 授权许可】

Unknown