4.6 Consider the differential equation y = y² subject to y(0) = 2. (a) What is the value of y from the predictor–corrector scheme after a single step h = 1/4? %3D

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4.6 Consider the differential equation y' = y? subject to y(0) = 2.
(a) What is the value of y from the predictor-corrector scheme after a
single step h = 1/4?
(b) It is easy to show that the exact value at x = 1/4 is y = 4. Based on
your result for a step size h = 1/4, what step size do we need to reduce
413
the error (defined as [ynumerical - Yexact) to a value of 1/8?
Transcribed Image Text:4.6 Consider the differential equation y' = y? subject to y(0) = 2. (a) What is the value of y from the predictor-corrector scheme after a single step h = 1/4? (b) It is easy to show that the exact value at x = 1/4 is y = 4. Based on your result for a step size h = 1/4, what step size do we need to reduce 413 the error (defined as [ynumerical - Yexact) to a value of 1/8?
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