Day 06

Thursday, Feb 16, 2017

Ch 2 Method of separation of variables, cont'd

2.3 1D heat equation with prescribed boundary values, cont'd

From last time:

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Example IBVP

Coefficients we computed:


Plotting solution with Python

(From 0 to 60mph in 20 minutes!)

numpy arrays, broadcasting, outer, linspace, arange, sum, base-0 counting, [1:]

functions (def), for loops

pylab, plot, xlabel, ylabel

Starting point:

%pylab inline
x = linspace(0,2*pi,5)
y = sin(x)
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See Plotting solution of heat equation IBVP.

Approximation by lowest-╬╗ solution

2.4 Some more examples of heat equation by separation of variables

2.4.1 No-flux BCs

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(Almost got to here.)

2.4.2 Circular bar

2.5 Laplace's equation in 2D


Decomposition trick