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# HW 1 - 1(exp(1/D − 1 1 Graph that exact solution for D =...

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MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering I Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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18.085 MATLAB 1 This homework is about convection-diffusion, an important equation. There will be a boundary layer of rapid change at one endpoint when the conditions are u (0) = u (1) = 0 and the u convection term dominates. The exact solution to Du �� + u = 1 is u = x (exp( x/D )
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Unformatted text preview: 1) / (exp(1 /D ) − 1). 1) Graph that exact solution for D = 1 / 25 2) Approximate − Du as usual by DK/h 2 (try 3 diﬀerent values of h ) 3) Approximate u by centered and forward and backward diﬀerences (same h ) 4) With f = ones(n,1) solve the matrix equations and label graphs of u 5) Write a SHORT conclusion from your tests—which method(s) to use ? 1...
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HW 1 - 1(exp(1/D − 1 1 Graph that exact solution for D =...

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