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HW_11-10-F - a step size of h = π/10 and the Euler method...

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ChE 348 Homework #11 _____________________________________Due: DO NOT TURN IN, for practice only 1. Write a computer program that solves each of the following initial value problem over the interval [0, 2], using the trapezoidal rule predictor-corrector with a sequence of grids h = 1/4, 1/8, and 1/16. Produce an orderly table of ( x n , y n ) pairs and discuss the errors. ( ) ( ) 2 2 2 1 ) ( : 0 ) 0 ( , 0 2 1 1 ' x x x y solution true y y x y + = = = + + 2. Using a hand calculator and h = 0.25, compute approximate solutions to the initial value problem 1 ) 0 ( , 4 1 ) 0 ( , 4 2 2 1 / 2 1 2 1 / 1 = = = + = y y y y y y y y Compute out to x = 1.0, using the Trapezoidal rule predictor-corrector method. 3. Consider the second-order equation 0 ) 0 ( , 8 1 ) 0 ( , 0 sin / // = = = + y y y y π ; write this as a first-order system and compute (by hand) approximate solutions using
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Unformatted text preview: a step size of h = π /10 and the Euler method. Show the first two steps. 4. Write a computer program that approximates the solution to the third order equation ; 3 ) ( , 1 ) ( , 1 ) ( , 8 10 2 2 5 4 // / 2 / // /// = − = = + + = + + + y y y x x y y y y using the following methods with h = 0.1 over the interval [0, 2]: (a) fourth-order Runge-Kutta (RK4) (b) Adams fourth-order predictor (AB4) and corrector (AM4) method with RK4 Compare the results with the true solution: 2 ) ( x e x y x + = −...
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