Analysis of a class of nonlinear integro-differential equations arising in a forestry application

Michael A. Kraemer, Leonid V. Kalachev

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)513-535
Number of pages23
JournalQuarterly of Applied Mathematics
Volume61
Issue number3
DOIs
StatePublished - Sep 2003

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