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**Approximations of the nonlinear Volterra’s population model by an efficient numerical method.**
*(English)*
Zbl 1223.92047

Summary: We apply the new homotopy perturbation method to solve the Volterra’s model for population growth of a species in a closed system. This technique is extended to give solutions for nonlinear integro-differential equations in which the integral term represents the total metabolism accumulated from time zero. The approximate analytical procedure only depends on two components. The new homotopy perturbation method was applied to nonlinear integro-differential equations directly and by converting the problem into nonlinear ordinary differential equation. We also compare this method with some other numerical results and show that the present approach is less computational and is applicable for solving nonlinear integro-differential equations and ordinary differential equations as well.

### MSC:

92D25 | Population dynamics (general) |

34K28 | Numerical approximation of solutions of functional-differential equations (MSC2010) |

45D05 | Volterra integral equations |

45J05 | Integro-ordinary differential equations |

65L03 | Numerical methods for functional-differential equations |

### Keywords:

integro-differential equation; population; new homotopy perturbation method (NHPM); growth; toxin
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\textit{N. A. Khan} et al., Math. Methods Appl. Sci. 34, No. 14, 1733--1738 (2011; Zbl 1223.92047)

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### References:

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