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Zbl 1038.65149
Parand, K.; Razzaghi, M.
Rational Chebyshev tau method for solving Volterra's population model. (English)
[J] Appl. Math. Comput. 149, No. 3, 893-900 (2004). ISSN 0096-3003

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

MSC 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations
92D25 Population dynamics

Keywords: Rational Chebyshev tau method; Volterra's population model; nonlinear integro-differential equation; numerical examples

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Zentralblatt MATH Berlin [Germany]