Solve a Partial Differential Equation Numerically - Maple Programming Help

Solve a Partial Differential Equation Numerically

 Description Solve a partial differential equation (PDE) numerically.

Enter a partial differential equation.

 > $\left(\frac{{ⅆ}}{{ⅆ}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{u}\left({x}{,}{t}\right)\right){-}\frac{{1}}{{10}}\left(\frac{{{ⅆ}}^{{2}}}{{ⅆ}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{{x}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{u}\left({x}{,}{t}\right)\right){=}{0}$
 $\frac{{\partial }}{{\partial }{t}}{}{u}{}\left({x}{,}{t}\right){-}\frac{{1}}{{10}}{}\frac{{{\partial }}^{{2}}}{{\partial }{{x}}^{{2}}}{}{u}{}\left({x}{,}{t}\right){=}{0}$ (1)

Enter the initial boundary conditions.

 > ${u}\left({x}{,}{0}\right){=}{1}{,}{u}\left({0}{,}{t}\right){=}{0}{,}{\mathrm{D}}\left[{1}\right]\left({u}\right)\left({1}{,}{t}\right){=}{0}$
 ${u}{}\left({x}{,}{0}\right){=}{1}{,}{u}{}\left({0}{,}{t}\right){=}{0}{,}{{\mathrm{D}}}_{{1}}{}\left({u}\right){}\left({1}{,}{t}\right){=}{0}$ (2)

Solve the equation.

 > $s:=\mathrm{pdsolve}\left(,\left\{\right\},\mathrm{numeric}\right):$

Plot the solution for select values of t.

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 > $\mathrm{plots}\left[\mathrm{display}\right]\left(\left\{\mathrm{p1},\mathrm{p2},\mathrm{p3},\mathrm{p4},\mathrm{p5}\right\},\mathrm{title}="Heat profile at t = 0, 0.1, 0.5, 1, 2"\right)$
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