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 = 0 . 6 and 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 ) = cos( x + y ). Applying formula (4) on page 135 of the text we compute ∂f ( x, y ) ∂x = ∂x [cos( x + y )] = sin( x + y ) ∂x ( x + y ) = sin( x + y ); ∂f ( x, y ) ∂y = ∂y [cos( x + y )] = sin( x + y ) ∂y ( x + y ) = sin( x + y ); f 2 ( x, y ) = ∂f ( x, y ) ∂x + ∂f ( x, y ) ∂y 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 ,
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