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HW3 - Fall 2010 Homework 3 EN 530.766 Rajat Mittal 1 Derive...

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Fall 2010 Rajat Mittal Homework 3 EN 530.766 1) Derive expressions for the modified wave number corresponding to 1 st derivative for the following schemes a. 2 nd -order central difference b. 4 th - order central difference c. 4 th –order Pade scheme 2) Derive the modified wavenumber for a second-order backward difference scheme. Note that the modified wavenumber in this case will be complex; i.e. '' ri kki k ' = + . a. Compare (and plot) the real part along with the real modified wavenumbers in the previous problem. b. Plot the imaginary part of the wavenumber on a separate plot. c. What is the possible effect of this complex part of the wavenumber on a
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