assignment3 - Instructor:Dr.EmreAlpman Assignment#3...

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ME 372 Computer-Aided Mechanical Engineering Instructor: Dr. Emre Alpman Assignment #3 Due Date: March 11th, 2010 SINGLE DEGREE-OF-FREEDOM SYSTEMS Summary of Previous Assignment Numerical solutions obtained with Forward and Backward Euler methods were compared to the  exact solution in figures 1, 2, 3 and 4 for step sizes 0.02, 0.04, 0.06 and 0.08 respectively. These figures  clearly show that Forward and Backward Euler schemes show some kind of an opposite behavior.  Backward Euler is more dissipative because the oscillations died out more quickly than the exact case.  On the other hand Forward Euler method yielded more oscillatory solutions. As the step size increased  the amplitude of the oscillations increased for Forward Euler however it decreased more for Backward  Euler. Eventually Forward Euler solution became unstable. Backward Euler solution did not have any  stability problem, however its accuracy degraded as the step size increased. Even for  h  = 0.02 there are  considerable discrepancies between Backward Euler solution and exact solution at the local extrema.  Although there are no stability restrictions on the step size for the implicit method, there are clearly  some accuracy restrictions. In order to obtain better accuracy a local error control was performed before 
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This note was uploaded on 04/05/2012 for the course MECHANICAL ME372 CAME taught by Professor Emraalpman during the Spring '10 term at Yeditepe Üniversitesi.

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assignment3 - Instructor:Dr.EmreAlpman Assignment#3...

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