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297_pdfsam_math 54 differential equation solutions odd

297_pdfsam_math 54 differential equation solutions odd -...

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Exercises 5.4 x 3 (1; 1) = 0 . 03125 . Repeating the algorithm with h = 2 1 , 2 2 , 2 3 we obtain the approximations in Table 5-E. Table 5–E : Approximations of the Solution to Problem 25. n h y (1) x 1 (1; 2 n ) 1 ) (1) n x 2 (1; 2 n ) 2 (1; 2 ) x 3 (1; 2 n ) 3 (1; 2 ) 0 1.0 1.29167 0.28125 0 . 03125 1 0.5 1.26039 0.34509 0 . 06642 2 0.25 1.25960 0.34696 0 . 06957 3 0.125 1.25958 0.34704 0 . 06971 We stopped at n = 3 since x 1 (1; 2 3 ) x 1 (1; 2 2 ) x 1 (1; 2 3 ) = 1 . 25958 1 . 25960 1 . 25958 = 0 . 00002 < 0 . 01 , x 2 (1; 2 3 ) x 2 (1; 2 2 ) x 2 (1; 2 3 ) = 0 . 34704 0 . 34696 0 . 34704 = 0 . 00023 < 0 . 01 , and x 3 (1; 2 3 ) x 3 (1; 2 2 ) x 3 (1; 2 3 ) = 0 . 06971 + 0 . 06957 0 . 06971 = 0 . 00201 < 0 . 01 . Hence y (1)
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