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Unformatted text preview: ld continue constructing a numerical method for solution of our initial value problem by means of another discretization, this time in the time
direction. We could do this via the familiar Cauchy-Euler method for ﬁnding
numerical solutions to the linear system (4.16). This method for ﬁnding approximate solutions to the heat equation is often called the method of ﬁnite
diﬀerences . With suﬃcient eﬀort, one could construct a computer program,
using Mathematica or some other software package, to implement it.
More advanced courses on numerical analysis often treat the ﬁnite diﬀerence
method in detail.3 For us, however, the main point of the method of ﬁnite
diﬀerences is that it provides considerable insight into the theory behind the
heat equation. It shows that the heat equation can be thought of as arising
from a system of ordinary diﬀerential equations when the number of dependent
variables goes to inﬁnity. It is sometimes the case that either a partial diﬀerential equation or a system of ordinary diﬀerential equations wi...
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This document was uploaded on 01/12/2014.
- Winter '14