Volume 19, Issue 4 (12-2022)
jor 2022, 19(4): 113-126 |
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Pourjafar S, Ayati Z. A New Optimal MVIM to Solve Two Biological Species System. jor 2022; 19 (4) :113-126
URL: http://jamlu.liau.ac.ir/article-1-2093-en.html
URL: http://jamlu.liau.ac.ir/article-1-2093-en.html
Department of Engineering Sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan, Rudsar-Vajargah, Iran
Abstract: (1708 Views)
In this paper, a new modified of well-known Variational Iteration Method (VIM) has been used to solve a system of integro-differential equations of predator-prey derived from the problem of two biological species living together. The error function has been obtained for each equation and consequently the maximum error on the supposed interval successively for iterations. We have also dissected the interval into n numbers of equal sub-interval and have chosen a special iteration of VIM by a suitable choice based on minimizing maximum error on the first sub-interval. Then, by using the selected iteration of the VIM, a new Multistep Variational Iteration Method has been applied to some steps. In the proposed method, VIM has been applied only on the first special sub-interval, and it has been used the value of the solution at the end of each step as the initial condition of the next step. In the end, we transmit the solution on each sub-interval to its real place. We have indicated that the error of the solution by the proposed method decreases significantly.
Keywords: Variational Iterative Method, Multistep Variational Iteration Method, System of Integro-differential Equations, Optimal Solution, Biological Species
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