derivation quiz 5

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4 Terms

1
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Given

d/dt T = alpha * d²/dx² T

2
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Step 1

d/dt T= (Ti+1 - Ti)/deltaT

3
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Step 2

d²/dx² T= (Ti+1-2Ti+Ti-1)/deltax²

4
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Step 3

(Ti,j+1-Ti,j)/deltat = alpha(Ti+1,j-2Ti,j + Ti-1,j)/deltax²

(Just the last equation he gives us divided by deltat on the left and subtracting Ti,j)