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lec36_12152006

# lec36_12152006 - 10.34 Numerical Methods Applied to...

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10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #36: TA-Led Final Review. BVP: Finite Differences or Method of Lines x C = Forward/Upwind/Central difference formulas 2 2 x C = Central difference-like Understand when to use the different formulas. Boundary Condition (Flux) D boundary x C =Reaction per surface area [moles/m 2 ·s] [m 2 /s] Internal Flux [(mol/m 3 )/m] A B The flux is the same for these two arrows can solve even if A and B are not known Partition function coefficient Figure 1. The flux is the same for arrows at A and B. Method of Lines Solve a differential equation along line i = 2, …, N-1 x C C x C 2 1 3 2 = Sparse Discretize y 1 2 3 x Boundary Condition may need to use shooting method Initial Condition gradient stiff in y-directon Figure 2. Example problem good for method of lines. If this is the B.C.: x C C x C Δ = 1 2 1 Use this additional equation with rest to solve for C 1 D.A.E. Cite as: William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

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Models vs. Data y = f(x , θ ) y 1 = f(x 1 , θ ) y 2 = f(x 2 , θ ) | y n = f(x n , θ ) Assumption: 1) y distributed normally around y ˆ 2) x are known exactly P(y) σ y ˆ y 10.34, Numerical Methods Applied to Chemical Engineering Lecture 36 Prof. William Green Page 2 of 6 Cite as: William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD
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