Homework 9 - BMED 2200 Modeling Biomedical Systems I Spring...

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± BMED 2200 Modeling Biomedical Systems I Spring 2008 Homework 9 Using the concepts developed in class for handling boundary conditions by finite difference methods, consider Challenge 2 where a patch is delivering a therapeutic to a receptor skin beneath the skin (problem 8.5 in the textbook). The governing equations, initial conditions, and boundary conditions for this diffusion problem are given in the class notes and in the text. For each of the boundary/interface conditions, derive the finite difference expression that will be used to process that boundary/interface condition. Using a sketch of the finite difference equation, as we have been doing in class, describe the order of calculations that will allow that boundary/interface condition to be processed. 1. Express the time derivative into forward finite difference: ! C ! t i , n = 1 " t ( C i , n + 1 # C i , n ) Express the second-order spatial derivative in terms of central finite differences: ) 2 ( 1 , 1 , , 1 2 , 2 2 n i n i n i n i C C C x x C ! + + ! " = # # Combine the above into each of the two partial differential equations and rearrange to solve for 1 , + n m i C BOE 1 , + n s i C : n m m m n m m m
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Homework 9 - BMED 2200 Modeling Biomedical Systems I Spring...

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