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:

2017_02_14/20170214_135432.jpg 2017_02_14/20170214_135509.jpg

Example IBVP

Coefficients we computed:

Bn_for_first_heat_solution.png

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)
plot(x,y)
2017_02_16/20170216_133326.jpg 2017_02_16/20170216_133330.jpg 2017_02_16/20170216_135457.jpg

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

2017_02_16/20170216_135438.jpg 2017_02_16/20170216_135444.jpg 2017_02_16/20170216_135506.jpg

(Almost got to here.)

2.4.2 Circular bar

2.5 Laplace's equation in 2D

BVP

Decomposition trick