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March 28, 2017

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Consider the initial value problem,

f(x,y) = y(18.06 - y), y(0) = 12.

The exact solution of the problem increases from y(0) =12 to y = 18.06 as x increases without limit.

Determine the minimum upper bound of h for the classical 4th-order Runge Kutta method to be absolutely stable for this problem. Give your answer to 3 decimal places.

Note : You can make use of table (3.1) of Study Unit 2 Numerical Methods for Differential Equations.

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