157_pdfsam_math 54 differential equation solutions odd

157_pdfsam_math 54 differential equation solutions odd -...

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Exercises 3.7 n =0 , 1 , 2 ,..., 35.) Lastly, we redo this work with K . 6and h =2 / 3. By so doing, we obtain the results given in the table in the answers of the text. (Note that the values for T 0 , T 6 , T 12 , T 18 , T 24 , T 30 ,and T 36 are given in the answers.) EXERCISES 3.7: Higher Order Numerical Methods: Taylor and Runge-Kutta, page 142 1. In this problem, f ( x, y )=co s ( x + y ). Applying formula (4) on page 135 of the text we compute ∂f ( x, y ) ∂x = [cos( x + y )] = sin( x + y ) ( x + y )= sin( x + y ); ( x, y ) ∂y = [cos( x + y )] = sin( x + y ) ( x + y sin( x + y ); f 2 ( x, y ( x, y ) + ± ( x, y ) ² f ( x, y sin( x + y )+[ sin( x + y )] cos( x + y ) = sin( x + y )[1 + cos( x + y )] , and so, with p = 2, (5) and (6) on page 135 yield x n +1 = x n + h, y n +1 = y n + h cos ( x n + y n ) h 2 2 sin ( x n + y n )[1+cos( x n +
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.

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