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**Rational Chebyshev tau method for solving Volterra’s population model.**
*(English)*
Zbl 1038.65149

Summary: An approximate 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 effect of toxin.

The approach is based on a rational Chebyshev tau method. The Volterra’s population model is first converted to a nonlinear ordinary differential equation. The operational matrices of derivative and product of rational Chebyshev functions are presented. These matrices together with the tau method are then utilized to reduce the solution of the Volterra’s model to the solution of a system of algebraic equations.

Illustrative examples are included to demonstrate the validity and applicability of the technique and a comparison is made with existing results.

The approach is based on a rational Chebyshev tau method. The Volterra’s population model is first converted to a nonlinear ordinary differential equation. The operational matrices of derivative and product of rational Chebyshev functions are presented. These matrices together with the tau method are then utilized to reduce the solution of the Volterra’s model to the solution of a system of algebraic equations.

Illustrative examples are included to demonstrate the validity and applicability of the technique and a comparison is made with existing results.

### MSC:

65R20 | Numerical methods for integral equations |

45J05 | Integro-ordinary differential equations |

45G10 | Other nonlinear integral equations |

92D25 | Population dynamics (general) |

### Keywords:

Rational Chebyshev tau method; Volterra’s population model; nonlinear integro-differential equation; numerical examples
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\textit{K. Parand} and \textit{M. Razzaghi}, Appl. Math. Comput. 149, No. 3, 893--900 (2004; Zbl 1038.65149)

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### References:

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