HW2 - MAE 290B, Winter 2010 HOMEWORK 2 Due Mon 01-25-2010...

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MAE 290B, Winter 2010 HOMEWORK 2 Due Mon 01-25-2010 in class Provide source codes used to solve all problems PROBLEM 1 Consider the non-linear ODE set d t u + 3 v 2 u - 3 w 2 v = sin(5 t ) , d t v + 10 u 3 v 3 - 2 uw - uvw 2 = 0 , d t w + 6 w 3 - 10 sin( uv 3 ) = 0 . with initial conditions u (0) = 1 , v (0) = 1 , w (0) = 1. 1. Find the numerical solution of the problem in the range 0 t 10 using (a) A RK3 scheme for Δ t = 0 . 1 , 0 . 01 , 0 . 001 , 0 . 0001. (b) A RK4 scheme for Δ t = 0 . 1 , 0 . 01 , 0 . 001 , 0 . 0001 and Δ t = 10 - 6 . 2. Consider that the solution from the RK4 scheme and Δ t = 10 - 6 as approximately exact. Use it as reference to calculate the error of the other solutions at t = 10, Err = | ( u (10) ,v (10) ,w (10)) - ( u RK 4 , Δ t =1 e - 6 (10) ,v RK 4 , Δ t =1 e - 6 (10) ,w RK 4 , Δ t =1 e - 6 (10)) | . Plot the error as a function of Δ t for both the RK3 and the RK4 schemes. Show that the error of the RK3 scheme goes as Δ t 3 while the error of the RK4 scheme goes as
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HW2 - MAE 290B, Winter 2010 HOMEWORK 2 Due Mon 01-25-2010...

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