# HW_09 - nonlinear boundary value problem 1 1 1 2 = = ≤...

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ChE 348 Homework # 9 _______________________________________________________________________ _ 1. Use a finite difference method (based on central differences) with a mesh size h = 0.25 to solve (by hand) the boundary value problem. . 2 ) 1 ( ) 0 ( 1 0 , ) 1 ( // = = = - + - y y x x y x y 2. Write a computer program that approximates the solutions of the linear boundary value problem . 1 ) ( ) 0 ( 1 0 , ) 3 cos 5 ( 2 // = = - = - pi y y x x y x y Using a finite difference method (based on central differences) with a sequence of grids, h = π /8, π /16, and π /32. Do the approximate solutions appear to be converging to a solution? 3. Use a shooting method combined with Euler’s method to solve (by hand) the
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Unformatted text preview: nonlinear boundary value problem. . 1 ) 1 ( ) ( 1 , 2 // = = ≤ ≤ = +-y y x x y y Show the first three iterations with a mesh size of h = 0.5. 4. Consider the nonlinear boundary value problem . 3 ) 2 ( , ) ( 2 , // = = ≤ ≤ = +-y y x x e y y Use the shooting method combined with the trapezoid rule predictor-corrector to construct solutions to this equation, and then use a forth-order Runge-Kutta scheme and compare the two approximate solutions. Are they nearly the same? Use a mesh size of h = 0.2....
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## This note was uploaded on 02/22/2010 for the course CHE 348 taught by Professor Chelikowsky during the Spring '08 term at University of Texas.

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