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# Category: Differential Equations
# Name: Fourier series animation (Gibbs phenomenon)
#
# Animation where a discontinuity appears and disappears to exhibit
# Gibbs phenomenon
#
# The computation can be slow, so be patient when running...
# The function (h is a parameter)
function F(x) = (
while x < -pi do increment x by 2*pi;
while x > pi do increment x by -2*pi;
if x < 0 then 2*h*(x+pi/2)/pi else 2-h
);
LinePlotWindow=[-pi*1.1,pi*1.1,-3,3];
LinePlotDrawLegends=false;
# For faster animation, precompute,
print("Precomputing Fourier Series...");
hvals = [0.0:0.1:2.0,2.0:-0.1:0.0];
for n=1 to elements(hvals) do (
h = hvals@(n);
printn (n + "/" + elements(hvals) + "...");
fs@(n) = NumericalFourierSeriesFunction (F, pi, 10);
);
print("Done... Starting animation...");
PlotWindowPresent(); # Make sure the window is raised
for k = 1 to 10 do (
for n = 1 to elements(hvals) do (
h = hvals@(n);
LinePlot(F, fs@(n))
)
)
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