149_pdfsam_math 54 differential equation solutions odd

149_pdfsam_math 54 differential equation solutions odd -...

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Exercises 3.6 0 0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 y x Figure 3–B : Polygonal line approximation to the solution of y 0 = x +3cos( xy ), y (0) = 0. A polygonal line, approximating the graph of the solution to the given initial value problem, which has vertices at points ( x, y ) from Table 3-C, is sketched in Figure 3-B. 13. We want to approximate the solution φ ( x )to y 0 =1 y + y 3 , y (0) = 0, at x =1 . (Inother words, we want to ±nd an approximate value for φ (1).) To do this, we will use the algorithm on page 130 of the text. (We assume that the reader has a programmable calculator or
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Unformatted text preview: executable program. Alternatively, the reader can use the software provided free with the text.) The inputs to the program are x = 0, y = 0, c = 1, = 0 . 003, and, say, M = 100. Notice that by Step 6 of the improved Eulers method with tolerance, the computations should terminate when two successive approximations dier by less that 0 . 003. The initial value for h in Step 1 of the improved Eulers method subroutine is h = (1 0)2 = 1 . For the given equation, we have f ( x, y ) = 1 y + y 3 , and so the numbers F and G in Step 3 145...
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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 University of California, Berkeley.

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