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Finite Difference Example

Finite Difference Example - Finite Difference Example Array...

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1 of 4 Finite Difference Example: Array Formulas in Excel The differential equation for one-dimensional, steady-state conduction with internal generation is 0 2 2 = + k q x T & with boundary conditions 0 , 1 = = x T T S L x T T S = = , 2 Using finite-difference approximations for the derivatives, k x q T T T n n n 2 1 1 2 Δ = + + & for interior nodes, and 0 , 2 1 2 2 1 = Δ = + x T k x q T T S & L x T k x q T T S N N = Δ = + , 2 2 2 1 & for the two “boundary” nodes. For nine nodes, the finite difference equations are Δ Δ Δ Δ Δ Δ Δ Δ Δ = 1 2 2 2 2 2 2 2 2 1 2 9 8 7 6 5 4 3 2 1 - - T T T T T T T T T 2 - 1 1 2 - 1 1 2 - 1 1 2 - 1 1
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