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Zbl 1156.65106
Marzban, H.R.; Hoseini, S.M.; Razzaghi, M.
Solution of Volterra's population model via block-pulse functions and Lagrange-interpolating polynomials. (English)
[J] Math. Methods Appl. Sci. 32, No. 2, 127-134 (2009). ISSN 0170-4214; ISSN 1099-1476/e

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

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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Zentralblatt MATH Berlin [Germany]