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Unformatted text preview: ε = 0) (b) Find the system of IVPs satisﬁed by the 3 ﬁrst terms (to order ε 2 ) of the Lindstedt-Poincar´ e perturbation series solution. (c) Solve those IVPs and choose the appropriate parameters so that no secular term arise from the 3 ﬁrst terms of the Lindstedt-Poincar´ e perturbation series solution. 3. ( 7 marks ) Consider the centrifuge problem : u ”( t )-ωu ( t ) = 0 , u (0) = 0 , u (2) = 20 . (1) a) Solve the centrifuge BVP by using an analytical version of the shooting method. 1 b) Suppose we use Heun’s 2 stage together with the shooting method to solve (1). What is the error between the exact shooting speed s and the approx-imate shooting speed s h . (Do not only apply the formula given in class, rederive it). If we want this error to be of at least 10-4 , what should be the order of Δ t ? (i.e. ﬁnd p such that Δ t = 10 p ). 2...
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This note was uploaded on 07/28/2009 for the course AMATH 351 taught by Professor Sivabalsivaloganathan during the Spring '08 term at Waterloo.
- Spring '08