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, ε = 0 . 003, and, say, M = 100. Notice that by Step 6 of the improved Euler’s method with tolerance, the computations should terminate when two successive approximations di²er by less that 0 . 003. The initial value for h in Step 1 of the improved Euler’s 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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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Approximation, Boundary value problem, ε

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