Composite spectral functions for solving Volterra’s population model. (English) Zbl 1127.92033

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 toxins. The approach is based upon composite spectral function approximations. The properties of composite spectral functions consisting of few terms of orthogonal functions are presented and are utilized to reduce the solution of the Volterra model to the solution of a system of algebraic equations. The method is easy to implement and yields very accurate result.


92D25 Population dynamics (general)
45J05 Integro-ordinary differential equations
34K07 Theoretical approximation of solutions to functional-differential equations
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