## 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.

## 10 Ways To Fight Off Cancer

Learning About 10 Ways Fight Off Cancer Can Have Amazing Benefits For Your Life The Best Tips On How To Keep This Killer At Bay Discovering that you or a loved one has cancer can be utterly terrifying. All the same, once you comprehend the causes of cancer and learn how to reverse those causes, you or your loved one may have more than a fighting chance of beating out cancer.

Get My Free Ebook