T 442 show that if the tension and density of a

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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.

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