Say you do two experiments where you apply one numerical method to approximate the solution of...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Say you do two experiments where you apply one numerical method to approximate the solution of an initial value problem fromt = 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 Say you do two experiments where you apply one numerical method to approximate the solution of an initial value problem fromt = 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
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
In most cases the solution of an initial value problem (1) exists in an x-interval larger than that guaranteed by the present theorems. Show this fact for y' = 2y 2 , y(1) = 1 by finding the best...
-
In Exercises 1-3, use the power method to approximate the dominant eigenvalue and eigenvector of A. Use the given initial vector x0, the specified number of iterations k, and three-decimal-place...
-
In Problems a-c, use the Bisection Method to approximate the real root of the given equation on the given interval. Each answer should be accurate to two decimal places. a. x3 + 2x - 6 = 0; [1, 2] b....
-
Our thoughts return to Ambrose and his nuts and berries. Ambroses utility function is U(x1, x2) = 4x1 + x2, where x1 is his consumption of nuts and x2 is his consumption of berries. (a) Let us find...
-
The Annapolis Rotary Club sells hot dogs for $1.95 each at the annual Annapolis Fall Fair. The Rotary Club buys wieners at $3.95 per package of 10 wieners, and hot dog buns at $2.90 per dozen. It...
-
A motor delivers 275 hp at 1000 rpm to the end of a shaft (see figure). The gears at B and C take out 125 and 150 hp, respectively. Determine the required diameter d of the shaft if the allowable...
-
Which of the following best describes the level of measurement of the earthquake depths described in Exercise 3: nominal, ordinal, interval, ratio? Exercise 3 In a test of the Atkins weight loss...
-
Bill and Hillary produce food and clothing. In an hour, Bill can produce 1 unit of food or 1 unit of clothing, while Hillary can produce 2 units of food or 3 units of clothing. They each work 10...
-
Given the resistance, create a plan of action for George and Ingmar using Kurt Lewin's model. Using the correct terminology be specific in outlining what you would do, including what you would...
-
State the predicted height, taken from your graph, of the ping pong ball bounce when dropped from 4 m. Then draw a sketch of the ping pong ball at the top of its bounce (maximum height) and give your...
-
. On November 1, YR01, Honda Co. issued $1,000 of 9% bonds payable at 108 plus accrued interest. The 2-year bonds are dated September 1, YR01, and mature on September 1, YR03. Honda paid...
-
On November 1, 2022, Charlie, Inc issued bonds to purchase a plot of agricultural land to be used for growing medical catnip which is newly allowed based on a binding referendum based on the election...
-
Aduro Clean Technologies has the following share outstanding since their initial share offering: 31,000 shares of $3 cumulative preferred shares 60,000 common shares issued at $10 each The board of...
-
TOPIC 1 : In reference to your current job (or a former one if you are currently not employed), please address the following: 1. Roughly what percentage of your work would you estimate to be of a...
-
Units produced is 1,500 Direct materials purchased is 19,000 board feet Direct materials issued into production is 17,200 board feet Standard cost per unit (12 board feet x $8) is $96 per unit...
-
On July 15, 2008, Michael and his wife Julie purchased a new home. They received the First-time Homebuyer Credit in the amount of $7,000. What tax form is used to repay their tax credit?
-
Which one of the following statements is true? O Even if convertible bondholders convert their investment to common stock, the bondholders still receive interest payments. There is no guarantee that...
-
Evaluate the line integral, where C is the given curve. C x 2 dx + y 2 dy, C consists of the arc of the circle x 2 + y 2 = 4 from (2, 0) to (0, 2) followed by the line segment from (0, 2) to (4, 3)
-
Give typical applications involving spanning trees.
-
All 3 x 2 matrices [ jk ] with first column any multiple of [3 0 -5] T .
-
Are the following functions harmonic? If our answer is yes, find a corresponding analytic function f(z) = u(x, y) + iv(x, y). v = (2x + 1)y
-
The unit-step response of a dynamic system is shown in Figure 10.12. Find the transfer function of the system if it can be approximated as \(a /\left(s^{2}+2 \zeta \omega_{n} s+\omega_{n}^{2}...
-
Consider the closed-loop control system shown in Figure 10.24. a. Using MATLAB, plot the unit-step responses of the system for the following values of \(K: 5,50\), and 500 . b. Compute the...
-
Use the Simulink block diagram built in Example 10.10 to find the unit-step responses for \(k_{\mathrm{I}}=50,500\), and 1550 . Set \(k_{\mathrm{p}}=250\) and \(k_{\mathrm{D}}=0\). Discuss the...
Study smarter with the SolutionInn App