Abstract
Certain models describing the age dynamics of a natural forest give rise to nonlinear integro-differential equations for the seedlings density as a function of time. The special feature of the problem is that corresponding solutions have non-smooth second derivatives. Since the biological model contains a small parameter, a perturbation method can be used to find an asymptotic solution. Banach's fixed point theorem is used to prove existence and uniqueness of the solution, the convergence of a numerical scheme, and the validity of the asymptotic approximation. In an example numerical and asymptotic approximations are compared for various choices of time steps.
Original language | English |
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Pages (from-to) | 513-535 |
Number of pages | 23 |
Journal | Quarterly of Applied Mathematics |
Volume | 61 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2003 |