Problem 10

Due in DSC 203 by 3 PM, Friday, November 02, 2001

In the past a class was given the following initial value problem:

$$\frac{dy}{dx}=x^2+y^2,\qquad\qquad y(0)=1.$$

They were asked to solve this numerically using Euler's method on the interval [0,1]. Not too long thereafter the students reported to the professor that their programs were terminating with an overflow error message. The error message indicated that the values were becoming too large to be stored in the computer.

Is this result due to the deficient computing power or is it an inherent property of the problem? Specifically show that there exists an a>0 such that $\lim\limits_{x\to a^-} y(x)=+\infty$.

Solutions, questions and/or comments should be directed to Judy Downey or Griff Elder

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Last modified:   Fri Oct 26 12:40:12 CDT 2001