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**Variational iteration method for autonomous ordinary differential systems.**
*(English)*
Zbl 1027.34009

Summary: Here, a new iteration technique is proposed to solve autonomous ordinary differential systems. In this method, general Lagrange multipliers are introduced to construct correction functionals for the systems. The multipliers in the functionals can be identified by the variational theory. The initial approximations can be freely chosen with possible unknown constants, which can be determined by imposing boundary/initial conditions. Some examples are given. The results reveal that the method is very effective and convenient.

### MSC:

34A45 | Theoretical approximation of solutions to ordinary differential equations |

34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |

### Keywords:

general Lagrange multipliers
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\textit{J.-H. He}, Appl. Math. Comput. 114, No. 2--3, 115--123 (2000; Zbl 1027.34009)

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### References:

[2] | He, J. H., A new approach to nonlinear partial differential equations, Communications in Nonlinear Science and Numerical Simulation, 2, 4, 230-235 (1997) |

[3] | He, J. H., Variational iteration method for delay differential equations, Communications in Nonlinear Science and Numerical Simulation, 2, 4, 235-236 (1997) |

[7] | He, J. H., A variational iteration method for nonlinearity and its applications (in Chinese), Mechanics and Application, 20, 1, 30-32 (1998) |

[8] | He, J. H., Variational iteration approach to 2-spring system (in Chinese), Mechanical Science and Technology, 17, 2, 221-223 (1998) |

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