Spatial Invasion of Pine Beetles Into Lodgepole Forests: A Numerical Approach

Document Type

Article

Journal/Book Title/Conference

SIAM Journal of Science Comp.

Volume

20

Issue

1

Publication Date

1998

First Page

164

Last Page

184

Abstract

We discuss a procedure for numerically approximating solutions to a system of nonlinear partial differential equations which describe mountain pine beetles attacking lodgepole pine {en masse}. A centered spatial discretization which yields a system of ordinary differential equations is presented, including a method for generating "transparent" spatial boundary conditions. A flux-based model estimates the phase speed of pheromone isoclines at the boundary, providing an overestimate of the flux of beetles across the boundaries and giving nearly transparent boundary conditions. An Adams variable-step predictor-corrector approach is applied to the discretized system. The numerical method and model are tested in both one and two space dimensions. In one space dimension a comparison of the solution using the flux estimates at the boundary is compared with a solution generated on a larger space domain. A spatially complicated example then is given to test the methodology in two dimensions.

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