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@fabern fabern commented Aug 4, 2025

Checklist

  • Appropriate tests were added
  • Any code changes were done in a way that does not break public API
  • All documentation related to code changes were updated
  • The new code follows the
    contributor guidelines, in particular the SciML Style Guide and
    COLPRAC.
  • Any new documentation only uses public API

Additional context

When simulating forests demographics as distribution n of trees of different sizes x we can use partial integro-differential equations. The integral reflects that the growth of a tree of size x depends on how much
sunlight 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:

$$\frac{\partial n(t,x)}{\partial t} = - \frac{\partial}{\partial x}\left[g(t,x) \int_{x}^{\infty} n(t,y) dy\right] - m(t,x)n(t,x),$$

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

@fabern fabern changed the title Add pide integral x to end Include PIDE integrals from x to the upper boundary of the domain Aug 4, 2025
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