HW5 - (a) What goes wrong at t = 2? Plot the backward Euler...

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MAT 421 Applied Computational Methods Prof. Gardner ( carl.gardner@asu.edu ), Goldwater 654 Reading :S e c t ion s1 .1 ,1 .7 ,4 .1–4 .4 ,3 .1–3 .3 ,6 .1–6 .4 ,7 .1–7 .4o fMoler’s Nu- merical Computing with MATLAB . Homework 5 Due: Fri Feb 10 (1) Verify the formulas in ivp1.m for y (FE), y y 2(TR)for y ± = - y , starting from the standard form for the di±erence methods: y n +1 = y n tf ( y n )( F o r w a r d E u l e r ) y n +1 = y n tf ( y n +1 )( B a c k w a r d E u l e r ) y n +1 = y n +
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Unformatted text preview: (a) What goes wrong at t = 2? Plot the backward Euler & TR numerical solutions. (b) What do the results for t = 2.1 illustrate? Plot the backward Euler & TR numerical solutions. (3) For du/dt = f ( u ), prove that the backward Euler method is rst-order accurate, using the denition of the local truncation error. Be sure to calcu-late the constant multiplying t in the global error....
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