che132a-rec-6 - Chemical Engineering 132A Analytical...

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Chemical Engineering 132A Analytical Methods of Chemical Engineering Professor Mike Gordon, Fall 2011 Mathematica Assignment #6: Visualizing PDE Solutions Commands for today Sum[f[n],{n,1,100}] Sum f[n] from n=1 to 100 ft=Table[f[n],{n,1,100}] Make a list of all f[n] for n=1-100, call the result ft ft[[5]] Pick out the 5 th element of the ft list Chop[] Chop will make really small terms identically =0 Animate[Plot[f[x,t],{x,0,1}],{t,0,1,0.1} ] Animate f[x,t], plot f[x,t] for z=0->1 and change t NIntegrate[f[x],{x,0,1},AccuracyGoal->8,MaxRecursions->20] Numerical integration for oscillatory functions Today we are going to visualize the solution to the 1D heat equation. We will consider a long, insulated bar with the temperate at each end fixed at 0 °C and some initial temperature distribution f(x) at t=0: 2 2 x T t T = α (1) 0 ) , ( ) , 0 ( = = t L T t T boundary conditions (2) ) ( ) 0 , ( x f x T = initial condition (3) Suppose our rod is length L=1, the thermal diffusivity 01 . 0 = α , and the initial temperature distribution is: < < = else everywhere 0 6 . 0 4 . 0 100 ) ( C x C x f o o (4)
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