The multistage variational iteration method for a class of nonlinear system of ODEs.

*(English)*Zbl 1132.34008The authors have employed the multistage variational iteration method (MVIM) to solve a system of first order differential equations with quadratic nonlinearity of the form

$$\frac{d{N}_{i}}{dt}={N}_{i}\left({b}_{i}+\sum _{j=1}^{m}{a}_{ij}{N}_{j}\right),\phantom{\rule{1.em}{0ex}}i=1,2,\cdots ,m,\phantom{\rule{2.em}{0ex}}(*)$$

subject to certain initial conditions. Earlier some authors have solved ($*$) by variational iteration method (VIM) on $[0,1]$. The present technique enables the authors to go for larger domain. Comparison of MVIM is made with VIM and fourth order Runge-Kutta method and the outcome seems to be satisfactory. In the conclusion, the authors have mentioned several advantages of MVIM over other methods. They are hopeful of applying MVIM to problems with oscillatory solutions in their future work.

Reviewer: Narahari Parhi (Bhubaneswar)

##### MSC:

34A45 | Theoretical approximation of solutions of ODE |

34A34 | Nonlinear ODE and systems, general |

34A12 | Initial value problems for ODE, existence, uniqueness, etc. of solutions |