assignment_4[1]

# assignment_4[1] - 4 0 , with initial condition 0, 1, 1 Use...

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1. [ ] 0 0 Find approximate numerical solutions on the interval 0,2 for the differential equation - 2 , with initial condition 0, 1 Use Euler's method, the mod dx t x t x dt = = = ( 29 ( 29 2 ified Euler method, and a fourth order Runge - Kutta method, each with step sizes 0.2, 0.1, and 0.05. 5 1 Show that 2 -1 is the exact solution to the initial value problem. 4 4 For t h x x t e t - = = = + each approximate solution provide a table, a graph, and the relative error at 1 and 2. t t = = 2 1 Find the two smallest positive roots of the equation cos , correct to seven 1 decimal places. (Suggestion: first graph the functions to see about where the roots lie.) x x e - = - + 3. 2. [ ] 2 2 0 0 0 2 Find approximate numerical solutions on the interval 0,1.2 for the differential equation
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Unformatted text preview: 4 0 , with initial condition 0, 1, 1 Use Euler's me d x x t x x dt + = = = = ( 29 thod with step sizes 0.2, 0.1, and 0.05. Then show that cos2 is the exact solution to the initial value problem. For each approximate solution provide a table, a graph, and the rel h x x t t = = = ative error at .5 and 1. t t = = 4. 2 2 3 x y-= 2 3 3 1 xy x-= The system, has a solution not too far from the point (1, 1). Find this root two ways. First using the two-dimensional version of Newtons method, and second by eliminating y , solving for x using the one-dimensional Newtons method, and substituting to find y . Math 400 Assignment #4 Due: May 11, 2010...
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## This note was uploaded on 09/16/2011 for the course MATH 400 taught by Professor Staff during the Spring '11 term at S.F. State.

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