Lineare partielle Differentialgleichungen 2. Ordnung

Parabolisch: Lösung mit Fourier

yx=(4/π)(∑_(n=0)^200)(1/(2n+1))Cos[((2n+1)/3)π]Sin[(2n+1)π x];

yxplot=Plot[yx,{x,-1,2},PlotRange->All,PlotPoints->100,BaseStyle->FontSize->16]

yx01plot=Plot[yx,{x,0,1},PlotRange->All,PlotPoints->100,BaseStyle->FontSize->16,PlotStyle->Red]

Show[yxplot,yx01plot]

uxt=(4/π)(∑_(n=0)^200)(1/(2n+1))Cos[((2n+1)/3)π]Sin[(2n+1)π x](E^(-(((2n+1))^2)(π^2)t));

Plot3D[Min[1,uxt],{x,0,1},{t,0,.05},PlotRange->All,PlotPoints->50,AxesLabel->{x,t,T},BaseStyle->FontSize->16]

Plot3D[uxt,{x,0,1},{t,0,.001},PlotRange->All,AxesLabel->{"x","t","Temperatur"}]

Plot[Table[uxt/.t->tt,{tt,{0.001,0.005,0.02,0.06,0.2}}]//Evaluate,{x,0,1},PlotRange->All,AxesLabel->{"x","Temperatur"},BaseStyle->FontSize->16]

Plot[Table[uxt/.x->xx,{xx,{0.02,0.1,0.2,0.3,0.34,0.5}}]//Evaluate,{t,0,.2},PlotRange->All,AxesLabel->{"t","Temperatur"},BaseStyle->FontSize->16]