# hw5 - justs its stepsizes to achieve || EST || where EST is...

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ME 210B Homework # 5 Due February 23, 2009 Test problems for Homework #5: 1. Predator-Prey Problem y 0 1 = . 25 y 1 - . 01 y 1 y 2 y 0 2 = - y 2 + . 01 y 1 y 2 for 0 t 10 with initial values y 1 = y 2 = 10. Plot y 1 vs. t and y 2 vs. t , and y 1 vs. y 2 . 2. Van der Pol’s equation y 0 1 = y 2 y 0 2 = η [(1 - y 2 1 ) y 2 - y 1 ] for 0 t 11 with initial values y 1 (0) = 2, y 2 (0) = 0. Plot y 1 vs. t and y 2 vs. t . Take η = 1. Homework problem: 1. (10 points) Consider the second-order method deﬁned by 0 | 0 0 1 | 1 0 | 1 2 1 2 along with its third-order error-estimating method 0 | 0 0 0 1 | 1 0 0 1 2 | 1 4 1 4 0 | 1 6 1 6 4 6 1

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Write a code based on the above embedded pair which adaptively ad-
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Unformatted text preview: justs its stepsizes to achieve || EST || , where EST is the estimate of the local error. Be sure to take advantage of the eciency associated with the construction of the embedded pair. Use your code to solve the test problems for = 10-3 , and = 10-5 . Plot the stepsize vs. time, for both values of . 2...
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hw5 - justs its stepsizes to achieve || EST || where EST is...

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