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

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.