HW_10-10-F - ChE 348 Homework # 10 _Due: Thursday, 18...

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ChE 348 Homework # 10 ___________________________________________Due: Thursday, 18 November 2010 1. Solve ( by hand ) the following problems using Euler’s method with a stepsize of h = 0.1. Compute the error using the true answer Y( x ). (a) [] ) arctan( ) ( 0 ) 0 ( , 5 . 0 0 , )) ( cos( ) ( 2 / x x Y Y x x Y x Y = = = (b) [] 2 2 2 / 1 ) ( 0 ) 0 ( , 5 . 0 0 , ) ( 2 1 1 ) ( x x x Y Y x x Y x x Y + = = + = 2. Using the approximation h x y x y x y x y n n n n 2 ) ( 3 ) ( 4 ) ( ) ( ' 1 1 1 + + derive the following numerical method for solving initial value problems. ) , ( 2 3 4 1 1 1 1 + = n n n n n y x hf y y y 3. Use the trapezoidal rule predictor-corrector with h = 0.1 to compute ( by hand ) approximate value of y (0.3) for the following initial value problems. () () 2 2 2 1 ) ( : 0 ) 0 ( , 0 2 1 1 ' x x x y solution true y y x y + = = = + + 4. Derive the numerical method based on using Simpson’s rule to approximate the
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This note was uploaded on 11/28/2010 for the course CHE 348 taught by Professor Chelikowsky during the Spring '08 term at University of Texas at Austin.

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