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Mathematica Plotting Issue

Posted 8 years ago
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I'm using Mathematica to solve an initial value problem, and then plot it. However, When I try and plot it I'm receiving an error message. The problem I'm trying to graph is enter image description here

Here is my code:

\[Kappa] = 1/4; L = 4; 
  f[x_] = Piecewise[{{100*Sin[Pi*x], 0 <= x < 2}, {0, 2 <= x < 4}}]
Plot[f[x], {x, 0, 4}, AxesLabel -> Automatic, PlotRange -> Full]
un[x_, t_, n_] = Exp[-1/4*(n Pi/4)^2 t] Sin[n Pi x/4]
an[n_] = 2/4 Integrate[f[x]*Sin[n Pi x/4], {x, 0, 4}]
an[n_] = Simplify[an[n], n \[Element] Integers]
u[x_, t_, m_] = Sum[an[n] un[x, t, n], {n, 1, m}]
Plot[{f[x], u[x, 0, 1]}, {x, 0, L}, AxesLabel -> Automatic, 
 PlotLegends -> "Expressions"]
Plot[{f[x], u[x, 0, 20]}, {x, 0, L}, AxesLabel -> Automatic, 
 PlotLegends -> "Expressions"]

The last part of my code, where I am trying to change the value of m is where I running into issues. How can I fix this? Thanks!

POSTED BY: Kim Wyluda

Have you tried with a delayed definition

u[x_, t_, m_] := Sum[an[n] un[x, t, n], {n, 1, m}]

? Mathematica may have trouble finding a closed form for the symbolic sum. With the delayed definition the sum in evaluated when the parameters are numeric, which is easier.

POSTED BY: Gianluca Gorni
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