Given  y'=2y, y(0)=1/2, and y(x)=1/2e2x.  Apply the Runge-Kutta method to approximate the solution of the following exact solution on the interval [0, 0.5] with step size h = 0.25. Show five-decimal place values of the approximate solution and actual solution at the point x = 0.25.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Given  y'=2y, y(0)=1/2, and y(x)=1/2e2x.  Apply the Runge-Kutta method to approximate the solution of the following exact solution on the interval [0, 0.5] with step size h = 0.25. Show five-decimal place values of the approximate solution and actual solution at the point x = 0.25.

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