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Unformatted text preview: MATH 2070U/2072U Test 7
Instructor: D.A. Aruliah Week 13, 2008
Name (last name, ﬁrst name): Student Number: Teaching Assistant: Instructions
• Before starting, read over the entire test carefully. • Please verify that the test has 5 pages. • You may use a calculator and a pen or pencil. • Test written in pencil are not elegible for regrading. • Laptops, cellphones, and pagers are not permitted. • Have your student card on your desk. • There are 4 questions on this test and a total of 20 marks. • There are 45 minutes for the test. • Questions do not carry equal weight so use your time wisely. • Show as much work as needed to fully answer the questions. • Write your answers as neatly as possible in the test itself. • You are expected to comply with the UOIT rules for academic conduct. Q: Mks: 1 4 2 6 3 6 4 4 Total 20 MATH 2070U/2072U Test 7 Page 2 of 5 1. [4 marks] Reduce the fourthorder initialvalue problem x(0) = −1, 1 x (0) = , 2 1 x (0) = 3 x − x ln(x ) − t2 = 0, to an equivalent ﬁrstorder system of ODEs 1. MATH 2070U/2072U 2. [6 marks] Consider the initialvalue problem Test 7 Page 3 of 5 y = y − t2 + 1 , ˙ y (1) = 0.25. Carry out two steps of Heun’s method with stepsize h = 0.1 to determine an approximate value y2 y (t2 ) = y (1.2). W! W! ]! X! W! W! ]! X! 2. MATH 2070U/2072U Test 7 Page 4 of 5 3. [6 marks] Consider the initialvalue problem for the system of ODEs du −u = , dt 1+v+u dv = −3v (v − u), dt u(0) = 0.2, v (0) = 0.11. Carry out one step of Euler’s method with stepsize h = 0.1 to determine approximate values for u1 u(t1 ) = u(0.1) and v1 v (t1 ) = v (0.1). 3. MATH 2070U/2072U Test 7 Page 5 of 5 4. [4 marks] Consider the initialvalue problem for the system of ODEs dX = −0.12X + 12Y dt dY = −3.6Y + 1.2 Z (1 − Z 2 ) − 1 , dt dZ 2 = −1.2Z + 6 Y + , dt X +1 X (0) = 0.125, Y (0) = 0.1, Z (0) = 0.15. Write out the M ATLAB commands required to produce a numerical solution of the given IVP on the interval 0 ≤ t ≤ 12. Use ode23 and an anonymous function. J!$ X] ? ] ] XWTER ! ? A ] !? ?8 = A ! SHI ] ] ] B A A J XWTER ] ...
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This note was uploaded on 02/23/2010 for the course MATH 2070 taught by Professor Aruliahdhavidhe during the Spring '10 term at UOIT.
 Spring '10
 aruliahdhavidhe
 Math

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