CHEN 3201 Lecture Notes - Lecture 47: Electronic Band Structure, Gaussian Elimination

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1st order rxn conservation/transport eqns this is conservation of mass this should be 1/s, right. Thiele modulus in book, it"s called damkholer number mistake in book, bu rxn part is in 2 terms, so have to take both into account. Chen3201_numericalmethods page 3: discretize space do centered differences, disicretize the bvp. 2 n unknowns want to interweave variables into a new variable that gives a new band structure. Chen3201_numericalmethods page 4 want to interweave variables into a new variable that gives a new band structure. Define vector z keeping i from 2:n - 1 center node for ci => z2i - 1 center node for ti => z2i concentration temperature. Write out the residual we set concentration and temperature to equal 1 in boundary conditions this keeps repeating size 2n. Jacobian is 2n x 2n & sparce (use banded gauss elimination to solve and also save on memory space)

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