2.5 Is there a range of timestep choices At where the error is roughly proportional to At“ (that is At to the power of four)? If so, what values of At does this apply for? What is the explanation for this? 2.6 Is there a range of timestep choices At where the error consistently does not improve even as n gets larger and At gets smaller? If so, what values of At does this apply for? 2.7 Now we will compare the efficiency of the Euler approach vs. the Runge-Kutta approach. To compare the cost, we can take the amount of work as how many times the function dydt is called. This is simply the number of steps for Euler and the number of steps times four for Runge-Kutta. Compare the amount of work required to achieve an error consistently better than one percent in each case (0.01). Only look at the output data you already have for powers of two for timestep and number of steps you have tried. 2.8 Compare the amount of work required to achieve an error consistently better than 0.01 percent in each case (0.0001). Consider only the powers of two for timestep and number of steps you have tried. Comment on the relative value of the two methods based on this work comparison.

2.5 Is there a range of timestep choices At where the error is roughly proportional to At“ (that is At to the power of four)? If so, what values of At does this apply for? What is the explanation for this? 2.6 Is there a range of timestep choices At where the error consistently does not improve even as n gets larger and At gets smaller? If so, what values of At does this apply for? 2.7 Now we will compare the efficiency of the Euler approach vs. the Runge-Kutta approach. To compare the cost, we can take the amount of work as how many times the function dydt is called. This is simply the number of steps for Euler and the number of steps times four for Runge-Kutta. Compare the amount of work required to achieve an error consistently better than one percent in each case (0.01). Only look at the output data you already have for powers of two for timestep and number of steps you have tried. 2.8 Compare the amount of work required to achieve an error consistently better than 0.01 percent in each case (0.0001). Consider only the powers of two for timestep and number of steps you have tried. Comment on the relative value of the two methods based on this work comparison.

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Description: 7.2 2.5 Is there a range of timestep choices At where the error is roughly proportional to At“(that is At to the power of four)? If so, what values of At does this apply for? What is theexplanation for this?2.6 Is there a range of timestep choices At

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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