M. Matinfar , Jafar-Nodeh ,
Volume 7, Issue 4 (1-2011)
Abstract
In this paper, He’s variational iteration method (VIM) is used to obtain approximate analytical solutions of the Abelian differential equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation and easily overcomes the difficulty of the perturbation technique or Adomian polynomials. The results reveal that VIM is very effective and simple.
S. Pourjafar, Z. Ayati,
Volume 19, Issue 4 (12-2022)
Abstract
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.
