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

✍ Scribed by H. R. Marzban; S. M. Hoseini; M. Razzaghi

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 74 KB
• Volume: 32
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1028

✦ Synopsis

Abstract

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. Copyright © 2008 John Wiley & Sons, Ltd.