CHEN 3201 Lecture Notes - Lecture 48: Backward Euler Method
28 Apr 2015
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Solution method = method of lines also involves finite differences, rk4, discretization) Chen3201_numericalmethods page 1 isn"t the concentration of the left side 1? also involves finite differences, rk4, discretization) Rk4 can be replaced by implicit euler c(0,t) = 0 c(1,t) = 0 c(x,0) = 0 for short time, use erf for long time, actually solve it we"re worried about long time. Convert w/ finite differences to a system of odes. Why is the top one 0? shouldn"t it be 1? middle part repeats this is a linear diff eq so we can write it as a matrix times a vector the above thing equals. Solve this using rk4 the k is the time element) for initial condition, we"d say evaluate k"s at old values of y. Only node 2 can change since all k values depend on 2nd node (for the red part) time step has to be much smaller than deltax.
