Assignment_4

Assignment_4 - t Plot the results and compare with(a...

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ME 303 ADVANCED ENGINEERING MATHEMATICS Assignment 4 Question 1. Consider the following first-order, initial value problem: 1 y x dx dy + = with 1 y(0) = a) Find the exact solution. ( Hint : one way is to introduce v = x + y) b) Find approximate values for () 5 . 0 = x y by applying each of the methods below with 25 . 0 = Δ x : i. Euler (explicit) ii. Euler predictor-corrector iii. 2 P nd P -order Runge-Kutta iv. 4 P th P -order Runge-Kutta Question 2. For the following first-order, initial value problem for ( ) t y : t y dt dy + = + 3 with 1 y(0) = a) Find the exact solution. b) Apply the 4 th order Runge-Kutta scheme to solve for ( ) t y on a spreadsheet. Use 1 . 0 = Δ t and solve for 2 0
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Unformatted text preview: t . Plot the results and compare with (a). Question 3. Derive a 2 P nd P-order Runge-Kutta formula that uses locations i x and x x x i c Δ + = 3 2 to calculate 1 + i y . (Read over the derivation handout, and just use the equations provided. There is no need to re-derive them from scratch). Question 4. Consider a second-order, initial value problem, 2 2 x y y y = + ′ + ′ ′ with 1 y(0) = , (0) y' = a) Find the exact solution. b) Rewrite as a set of first order ODEs. Apply 2 P nd P-order Runge-Kutta scheme to find ( ) 2 . = x y using 1 . = Δ x ....
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This note was uploaded on 09/16/2011 for the course ME 303 taught by Professor Serhiyyarusevych during the Spring '10 term at Waterloo.

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