Solved: itial-value problem. First use Euler’s method and

Chapter 2, Problem 12E

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QUESTION:

In Problems 11 and 12 use a numerical solver to obtain a numerical solution curve for the given initial-value problem. First use Euler’s method and then the RK4 method. Use h = 0.25 in each case. Superimpose both solution curves on the same coordinate axes. If possible, use a different color for each curve. Repeat, using h = 0.1 and h = 0.05.

\(y^{\prime}=y(10-2 y)\),        y(0)=1

Text Transcription:

y^prime=y(10-2y)

Questions & Answers

QUESTION:

In Problems 11 and 12 use a numerical solver to obtain a numerical solution curve for the given initial-value problem. First use Euler’s method and then the RK4 method. Use h = 0.25 in each case. Superimpose both solution curves on the same coordinate axes. If possible, use a different color for each curve. Repeat, using h = 0.1 and h = 0.05.

\(y^{\prime}=y(10-2 y)\),        y(0)=1

Text Transcription:

y^prime=y(10-2y)

ANSWER:

Step 1 of 4

The approximation Euler method (color red) and the approximation fourth-order Runge-Kutta (color blue) are shown in the graph below. We see that the Euler method has difficulty approximating the solution with this particular step size while fourth-order Runge-Kutta does not have the same difficulty.

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