Include PIDE integrals from x
to the upper boundary of the domain
#459
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Checklist
contributor guidelines, in particular the SciML Style Guide and
COLPRAC.
Additional context
When simulating forests demographics as distribution
n
of trees of different sizesx
we can use partial integro-differential equations. The integral reflects that the growth of a tree of sizex
depends on how muchsunlight it obtains, which depends on how many trees are larger than
x
(e.g. see Lehmann et al. (2015)).To be able to simulate these kind of systems, MethodOfLines.jl needs to be able to simulate PIDEs of the form:
where$g$ represent the growth (i.e. advection into higher size classes $x$ ) and $m$ represents a mortality rate.
Currently MethodOfLines.jl supports integrals from the lower boundary up to$x$ (PR #216) but not from $x$ to the upper boundary.
The present PR extends MethodOfLines.jl capabilities to simulating integrals from$x$ to the upper boundary.
This solves #432