An ODE Is Solved Numerically Three Different Ways, Each Using A Time Step Of T=0.1 (Euler's Method, The Midpoint Method And A 4th Order Runge Kutta Method), And Then Again Using T=0.1 . The Solution Is NOT Shown! (neither Is The Problem!) However, The Errors In The Solution (measured At T = 10) Using That Time Step Are Shown In The Table Below: Euler Error Midpoint Error Runge-Kutta Error 1 1.3 0.20 0.05 0.1 0.13 0.0020 5 X 10^6 For Each Method, Write An Approximate Function Which Describes How The Error Varies With Time-step .

An ODE is solved numerically three different ways, each using a time step of t=0.1 (Euler’s method, the midpoint method and a 4th order Runge Kutta method), and then again using t=0.1 . The solution is NOT shown! (neither is the problem!) However, the errors in the solution (measured at t = 10) using that time step are shown in the table below: Euler Error Midpoint Error Runge-Kutta Error 1 1.3 0.20 0.05 0.1 0.13 0.0020 5 x 10^6 For each method, write an approximate function which describes how the error varies with time-step .

- October 10, 2022 - Edwin Tunner

An ODE is solved numerically three different ways, each using a time step of t=0.1 (Euler’s method, the midpoint method and a 4th order Runge Kutta method), and then again using t=0.1 . The solution is NOT shown! (neither is the problem!) However, the errors in the solution (measured at t = 10) using that time step are shown in the table below:

	Euler Error	Midpoint Error	Runge-Kutta Error
1	1.3	0.20	0.05
0.1	0.13	0.0020	5 x 10^6

For each method, write an approximate function which describes how the error varies with time-step .

E_euler = …

E_mp = …

E_rk4 = …

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