2.3.3 From Mathematica help pages

problem number 85

Taken from Mathematica DSolve help pages

Initial value problem with Dirichlet boundary conditions. 1D, zero potential.

Solve for \(f(x,t)\) \[ I f_t = - 2 f_{xx} \] With boundary conditions \begin {align*} f(5,t) &= 0\\ f(10,t) &=0 \\ \end {align*}

And initial conditions \(f(x,2)=f(x)\) where \(f(x)=-350 + 155 x - 22 x^2 + x^3\)

pict
Figure 2.18:PDE specification

Mathematica


\[\left \{\left \{f(x,t)\to \underset {n=1}{\overset {\infty }{\sum }}\frac {100 \left (7+8 (-1)^n\right ) e^{-\frac {2}{25} i n^2 \pi ^2 (t-2)} \sin \left (\frac {1}{5} n \pi (x-5)\right )}{n^3 \pi ^3}\right \}\right \}\]

Maple


\[f \left (x , t\right ) = \Mapleoverset {\infty }{\Mapleunderset {n =1}{\sum }}\frac {\left (800 \left (-1\right )^{n}+700\right ) {\mathrm e}^{-\frac {2 i \pi ^{2} \left (t -2\right ) n^{2}}{25}} \sin \left (\frac {\pi \left (x -5\right ) n}{5}\right )}{\pi ^{3} n^{3}}\]

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