Say you do two experiments where you apply one numerical method to approximate the solution of an initial value problem from t = 6 tot = 15, first using the stepsize At = h and then using the stepsize At = h/11 (so, taking 11 times more steps). If E¡ and E, are the errors in the respective approximations for y(15), what approximate number would you expect the ratio of the errors # to be if you were using the following numerical methods? (Alternatively: For the error in the second approximation, by approximately what factor would you expect the (global) truncation error of our first approximation to be cut?) Euler's method: Improved Euler's method: (Classical) 4th-order Runge-Kutta

Say you do two experiments where you apply one numerical method to approximate the solution of an initial value problem from t = 6 tot = 15, first using the stepsize At = h and then using the stepsize At = h/11 (so, taking 11 times more steps). If E¡ and E, are the errors in the respective approximations for y(15), what approximate number would you expect the ratio of the errors # to be if you were using the following numerical methods? (Alternatively: For the error in the second approximation, by approximately what factor would you expect the (global) truncation error of our first approximation to be cut?) Euler's method: Improved Euler's method: (Classical) 4th-order Runge-Kutta

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Say you do two experiments where you apply one numerical method to approximate the solution of an initial value problem from t = 6 to t = 15, first using the stepsize At = h and then using the stepsize
At = h/11 (so, taking 11 times more steps). If E, and E, are the errors in the respective approximations for y(15), what approximate number would you expect the ratio of the errors
E,
to be if you were
using the following numerical methods?
(Alternatively: For the error in the second approximation, by approximately what factor would you expect the (global) truncation error of our first approximation to be cut?)
Euler's method:
Improved Euler's method:
(Classical) 4th-order Runge-Kutta

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