In mathematics, the additive Schwarz method, named after Hermann Schwarz, solves a boundary value problem for a partial differential equation approximately by splitting it into boundary value problems on smaller domains and adding the results.
Partial differential equations (PDEs) are used in all sciences to model phenomena.
Even if the reader is unfamiliar with the notation, the purpose is merely to show what a BVP looks like when written down.
The goal of the computer program would be to calculate the value of f at those 64 points, which seems easier than finding an abstract function of the square.
There are some difficulties, for instance it is not possible to calculate fxx(0.5,0.5) knowing f at only 64 points in the square.
If we split the domain [0,1] × [0,1] into two subdomains [0,0.5] × [0,1] and [0.5,1] × [0,1], each has only half of the sample points.
Here we assume that the reader is familiar with partial differential equations.
We will be solving the partial differential equation We impose boundedness at infinity.