Heqat Diffusion in Python

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$\begin{bmatrix} 1+s & -0.5s & 0 \\ -0.5s & 1+s & -0.5s \\ 0 & -0.5s & 1+s \end{bmatrix} \times \left[ \begin{array}{c} T[1,1] \\ T[1,2] \\ T[1,3] \end{array} \right] = \begin{bmatrix} 1-s & 0.5s & 0 \\ 0.5s & 1-s & 0.5s \\ 0 & 0.5s & 1-s \end{bmatrix} \times \left[ \begin{array}{c} T[0,1] \\ T[0,2] \\ T[0,3] \end{array} \right] + \left[ \begin{array}{c} 0.5sT[1,0]+0.5sT[0,0] \\ 0 \\ 0.5sT[1,4]+0.5sT[0,4] \end{array} \right]$

Exploring the diffusion equation with Python « Hindered Settling

$\begin{array}{rrrrrcl} -sT[1,0]&+(1+2s)T[1,1]&-sT[1,2]&+0T[1,3]&+0T[1,4]&=&T[0,1] \\ 0T[1,0]&-sT[1,1]&+(1+2s)T[1,2]&-sT[1,3]&+0T[1,4]&=&T[0,2] \\ 0T[1,0]&+0T[1,1]&-sT[1,2]&+(1+2s)T[1,3]&-sT[1,4]&=&T[0,3] \end{array}$

Exploring the diffusion equation with Python « Hindered Settling

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$\begin{array}{rrrrrcl} -0.5sT[1,0] & +(1+s)T[1,1] & -0.5sT[1,2] & = & 0.5sT[0,0] & +(1-s)T[0,1] & +0.5sT[0,2] \\ -0.5sT[1,1] & +(1+s)T[1,2] & -0.5sT[1,3] & = & 0.5sT[0,1] & +(1-s)T[0,2] & +0.5sT[0,3] \\ -0.5sT[1,2] & +(1+s)T[1,3] & -0.5sT[1,4] & = & 0.5sT[0,2] & +(1-s)T[0,3] & +0.5sT[0,4] \end{array}$

Exploring the diffusion equation with Python « Hindered Settling

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$0.5s\big(T[n+1,j+1]-2T[n+1,j]+T[n+1,j-1]\big) + 0.5s\big(T[n,j+1]-2T[n,j]+T[n,j-1]\big) = T[n+1,j]-T[n,j]$

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$\begin{array}{rrrrcrr} (1+2s)T[1,1]&-sT[1,2]&+0T[1,3]&=&T[0,1]&+sT[1,0] \\ -sT[1,1]&+(1+2s)T[1,2]&-sT[1,3]&=&T[0,2]& \\ 0T[1,1]&-sT[1,2]&+(1+2s)T[1,3]&=&T[0,3]&+sT[1,4] \end{array}$

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Heqat Diffusion in Python

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