Solving nonlocal initial-boundary value problems for the Lotka–von Foerster model

• Published in: Applied mathematics and computation Vol. 225; pp. 7 - 15
• Main Authors: Bougoffa, Lazhar, Rach, Randolph C., Wazwaz, Abdul-Majid
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2013
• Subjects: Adomian decomposition method; First-order hyperbolic partial differential equations; Lotka–von Foerster model; Nonlocal initial-boundary value problems; Lotka–von Foerster model; Nonlocal initial-boundary value problems; Adomian decomposition method; First-order hyperbolic partial differential equations
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2013.09.003

In this paper, we present a new approach to solve nonlocal initial-boundary value problems for the Lotka–von Foerster model subject to initial and nonlocal boundary conditions of integral type. We first transform the given nonlocal initial-boundary value problem into an equivalent local initial-boundary value problem. Then we apply a modified Adomian decomposition method, which permits convenient resolution of these problems. Also a new method is developed to solve this nonlocal model, which reduces it to an equivalent local initial-boundary value problem for a system of ordinary differential equations.