Solution of Volterra’s population model via block-pulse functions and Lagrange-interpolating polynomials.

*(English)*Zbl 1156.65106Summary: A numerical method for solving Volterra’s population model for population growth of a species in a closed system is proposed. Volterra’s model is a nonlinear integro-differential equation where the integral term represents the effects of toxin. The approach is based on hybrid function approximations. The properties of hybrid functions that consist of block-pulse and Lagrange-interpolating polynomials are presented. The associated operational matrices of integration and product are then utilized to reduce the solution of Volterra’s model to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. Applications are demonstrated through an illustrative example.

##### MSC:

65R20 | Numerical methods for integral equations |

45J05 | Integro-ordinary differential equations |

45G10 | Other nonlinear integral equations |

92D25 | Population dynamics (general) |

##### Keywords:

Volterra’s population model; hybrid function; block-pulse functions; Lagrange-interpolating polynomials; nonlinear integro-differential equation; orthogonal functions; numerical examples
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\textit{H. R. Marzban} et al., Math. Methods Appl. Sci. 32, No. 2, 127--134 (2009; Zbl 1156.65106)

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