Solution Found!
Solved: itial-value problem. First use Euler’s method and
Chapter 2, Problem 12E(choose chapter or problem)
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.