288_pdfsam_math 54 differential equation solutions odd

288_pdfsam_math 54 differential equation solutions odd -...

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Chapter 5 we obtain a system in normal form x 0 1 = x 2 , x 0 2 = x 3 , x 0 3 = x 4 + t, x 0 4 = x 5 , x 0 5 = 1 5 (2 x 4 2 x 3 +1) with initial conditions x 1 (0) = x 2 (0) = x 3 (0) = 4 ,x 4 (0) = x 5 (0) = 1 . 9. To see how the improved Euler’s method can be extended let’s recall, from Section 3.6, the improved Euler’s method (pages 127–128 of the text). For the initial value problem x 0 = f ( t, x ) ( t 0 )= x 0 , the recursive formulas for the improved Euler’s method are t n +1 = t n + h, x n +1 = x n + h 2 [ f ( t n n )+ f ( t n + h, x n + hf ( t n n ))] , where h is the step size. Now suppose we want to approximate the solution x 1 ( t ), x 2 ( t )tothe system x 0 1 = f 1 ( t, x 1 2 )a n
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