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 .

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

See similar textbooks

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