151_pdfsam_math 54 differential equation solutions odd

151_pdfsam_math 54 differential equation solutions odd -...

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Exercises 3.6 Table 3–D : Improved Euler’s method approximations to φ (1), where φ ( x )istheso lut ion to y 0 =1 y + y 3 , y (0) = 0. h y (1; h ) φ (1) y (1; h ) (1; h ) φ (1) 11 . 0 2 1 0.7372229 2 2 0.7194115 2 3 0.7169839 y =0 . 40625 + 0 . 25(0 . 6607971 + 0 . 6630946) 0 . 7372229 . Thus the approximate value of the solution at x =1i s0 . 7372229. Further outputs of the algorithm are given in Table 3-D. Since ± ± y (1; 2 3 ) y (1; 2 2 ) ± ± = | 0 . 7169839 0 . 7194115 | < 0 . 003 , the algorithm stops (see Step 6 of the improved Euler’s method with tolerance) and prints out that φ (1) is approximately 0 . 71698. 15. For this problem, f ( x, y )=( x + y +2) 2 . We want to approximate the solution, satisfying y (0) = 2, on the interval [0 , 1
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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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