orego - ODE - Problem OREGO II-9-1 9 Problem OREGO 9.1...

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Unformatted text preview: ODE - Problem OREGO II-9-1 9 Problem OREGO 9.1 General information The problem consists of a sti system of 3 non-linear Ordinary Di erential Equations. The name Orego was given by Hairer & Wanner [ HW96 ] and refers to the Oregonator model which is described by this ODE. The Oregonator model takes its name from the University of Oregon where in the 1972 Field, K or os & Noyes [ FKN72 ] proposed this model for the Belousov{Zhabotinskii reaction. The INdAM-Bari Test Set group contributed this problem to the test set. The software part of the problem is in the le orego.f available at [ MI03 ]. 9.2 Mathematical description of the problem The problem is of the form d y d t = f ( y ) ; y (0) = y ; with y 2 R 3 ; t 360 : The function f is de ned by f ( y ) = B @ s ( y 2 y 1 y 2 + y 1 qy 2 1 ) 1 s ( y 2 y 1 y 2 + y 3 ) w ( y 1 y 3 ) 1 C A : The values of the parameters s , q and w are s = 77 : 27 w = 0 : 161 q = 8 : 375 10 6 : The initial vector y is given by (1 ; 2 ; 3) T . 9.3 Origin of the problem The OREGO problem originates from the celebrated Belousov{Zhabotinskii (BZ) reaction. When certain reactans, like bromous acid, bromide ion and cerium ion, are combined, they exhibit a chemical reaction which, after an induction period of inactivity, oscillates with change in structure and in color, from red to blue and viceversa. The color changes are caused by alternating oxidation{reductions in which the cerium switches its oxidation state from Ce(III) to Ce(IV)....
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This note was uploaded on 07/08/2009 for the course ME 210B taught by Professor Linda during the Spring '09 term at UCSB.

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orego - ODE - Problem OREGO II-9-1 9 Problem OREGO 9.1...

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