DEVELOPMENT AND ANALYSIS OF QUADRATURE
AND GALERKIN METHODS FOR APPROXIMATE
SOLUTION TO THE INTEGRAL FORMULATION
OF VOLTERRA'S POPULATION EQUATION WITH
DIFFUSION AND NOISE

Wyatt D. Sharp, Edward J. Allen
Raytheon
Springfield, Virginia 22150, USA
e-mails: wsharp@softhome.net, Wyatt_D_Sharp@Raytheon.com
Department of Mathematics and Statistics
Texas Tech University
Lubbock, Texas 79409-1042, USA
e-mail: eallen@math.ttu.edu

Abstract.In this research, an equivalent integral formulation of Volterra's population equation with diffusion and noise is numerically studied. The noise term in time and space is represented through a Brownian sheet. Two independent numerical methods are developed to solve this integral equation, a quadrature method and a semi-discrete Galerkin procedure. Error analyses for the two methods are performed which prove convergence of the approximations to the exact solution. Three numerical examples are given which confirm the results of the error analyses.

Received: January 10, 2003

AMS Subject Classification: 65C30, 60H35, 92D25

Key Words and Phrases: stochastic partial differential equation, population dynamics, quadrature method, Galerkin method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 4
Issue: 4