eml4312 midterm (3)

# eml4312 midterm (3) - EGM 4313 – Midterm Exam NAME 2...

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Unformatted text preview: EGM 4313 – Midterm Exam NAME:____________________________________ 2 hours – Open book, closed notes, no calculators 1. Consider 2 x y x y = ⋅ + ′ ′ subject to the initial conditions 1 ) ( , ) ( = ′ = y y . (a) Write this differential equation and initial conditions as a system of first order differential equations with initial conditions. ( ) ( ) . 1 , , . , 2 1 1 2 2 2 1 2 1 1 = = ⋅ − = ′ = ′ = y y y x x y y y y y y y Let (b) Write the 4 th order Runge-Kutta equations for the numerical solution of this system with a fixed step size of 0.001. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 4 3 2 1 2 1 2 1 1 3 1 2 2 3 4 1 2 1 2 2 2 3 1 1 1 2 2 1 2 1 2 2 1 2 2 6 1 001 . 001 . 001 . 2 1 0005 . 0005 . 2 1 001 . 2 1 0005 . 0005 . 2 1 001 . , 001 . 1 1 2 2 2 k k k k y y y y k y x x k y k k y x x k y k k y x x k y k y x x y k n n n n n n n n n n n n n n n n n n n n + ⋅ + ⋅ + ⋅ + =...
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eml4312 midterm (3) - EGM 4313 – Midterm Exam NAME 2...

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