## Operator Splitting Methods

Suppose one has an evolution equation of a general form u — A1 + A2 [22]

where each of A1 and A2 may depend on x, t, u, 8xu, etc. The criterion by which the RHS of [22] has been broken down into the two terms is this: each of the auxiliary problems u = Ak, k = 1, 2

can be solved easily. Then, to approximate the solution of [22], one solves the two individual equations [23] in sequence over each time step. The global error generated by this splitting is 0(t), in addition to any errors that may be introduced when solving each of the [23]. More accurate versions of this method are also available. However, we do not advocate for operator-splitting methods because of their stability properties. Namely, although for linear equations such methods are unconditionally stable, for nonlinear equations, in general, the stability of operator-splitting methods is determined by a condition similar to [8], even if each of eqns [23] is solved exactly. Hence, in such cases, operator-splitting methods offer no advantage over explicit methods. Operator-splitting methods find their primary use in solving (nonlinear) wave equations without dissipation, which, however, do not normally occur in ecological models.

Was this article helpful?

Get All The Support And Guidance You Need To Be A Success At Helping Save The Earth. This Book Is One Of The Most Valuable Resources In The World When It Comes To How To Recycle to Create a Better Future for Our Children.

Get My Free Ebook

## Post a comment