Abstract:
Numerical methods are a eld of mathematics concerned with the creation of
mathematical tools to solve applied problems. In this paper, we concentrate
on multigrid methods, an approach that can be used for solving systems of lin-
ear equations that arise from discretizing ordinary di erential equations, among
many other things. Multigrid methods are an advanced topic not usually taught
to undergraduates. Furthermore, self-learning is made challenging as most exist-
ing literature is written in a style typical to mathematics, which can be di cult
to decipher for the inexperienced. However, the core concepts behind multigrid
can be easily understood. In this paper, I provide introductions to these cen-
tral ideas (iterative methods and the smoothing property, coarse grids, residual
correction, transfer operators, and recursion), with the intention of bridging
the knowledge gap that exists before more popular multigrid literature can be
approached.
