Show that the Midpoint method and the Modified Euler method give the same approximations to the initial-value

Question:

Show that the Midpoint method and the Modified Euler method give the same approximations to the initial-value problem
y' = −y + t + 1, 0 ≤ t ≤ 1, y(0) = 1,
For any choice of h. Why is this true?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Numerical Analysis

ISBN: 978-0538733519

9th edition

Authors: Richard L. Burden, J. Douglas Faires

See More Books

Question Posted: Mar 22, 2016 02:49 AM

See More Questions

Use the Modified Euler method to approximate the solutions to each of the following initial-value problems, and compare the results to the actual values. a. y' = te3t 2y, 0 t 1, y(0) = 0, with...
Use the Modified Euler method to approximate the solutions to each of the following initial-value problems, and compare the results to the actual values. a. y' = ety, 0 t 1, y(0) = 1, with h = 0.5;...
Use the Modified Euler method to approximate the solutions to each of the following initial-value problems, and compare the results to the actual values. a. y' = y/t (y/t)2, 1 t 2, y(1) = 1, with h...
Scott incorporates his sole proprietorship as Superior Corporation and transfers its assets to Superior in exchange for all 100 shares of Superior stock and four $7,500 interest-bearing notes. The...
Why do many experts regard the telephone as a key instrument in the delivery of financial services in the future? What advantages does the telephone have over other service-delivery vehicles?
Researchers conducted a study that compared two groups on a scale variable, and reported a confidence interval around the difference between means of [- 0.26, 1.74] a. Would the researchers report...
Become familiar with the key features of life insurance policies. L01
The financial statements of P&G are presented in Appendix B. The companys complete annual report, including the notes to the financial statements, is available online. Instructions Refer to P&Gs...
Waterway Inc. reported the following pretax income (loss) and related tax rates during the years 20192022. Pretax Income (loss) Tax Rate 2019 $92,800 40 % 2020 (208,800) 40 % 2021 232,000 20 % 2022...
1. Treating year as the independent variable and the winning value as the dependent variable, find linear equations relating these variables (separately for men and women) using the data for the...
Use the results of Exercise 16 and Cubic Hermite interpolation to approximate values of y(t), and compare the approximations to the actual values. a. y(0.54) and y(0.94) b. y(1.25) and y(1.93) c....
Show that the difference method w0 = , wi+1 = wi + a1f (ti ,wi) + a2f (ti + 2,w1 + 2f (ti ,wi)), For each i = 0, 1. . . N 1, cannot have local truncation error O (h3) for any choice of constants a1,...
a. What is the variance? b. What are the measurement units of the variance? c. Which is the more easily interpreted variability measure, the standard deviation or the variance? Why? d. Once you know...
Sunn Company manufactures a single product that sells for $180 per unit and whose variable costs are $141 per unit. The company's annual fixed costs are $636,000. The sales manager predicts that next...
Question 22(5 points) Silver Corp. declares a 15% stock dividend to its shareholders on 1/18. On that date, the company had 15,000 shares issued and 12,000 shares outstanding. Silver Corp. common...
Select your a diagnosis from the DSM-5. using your information found through a search of the literature available on your selected diagnosis using appropriate references of peer reviewed journal...
Problem 1: Grand Monde Company manufactures various lines of bicycles. Because of the high volume of each type of product, the company employs a process cost system using the FIFO method to determine...
Draw the shear force, bending moment diagram of a beam for the loading condition as shown in the figure. Determine the maximum bending moment, and shear force in the beam. Support reactions are pre-...
In the Lakdawalla-Philipson model, why do the authors claim that the minimum average cost of the for-profi t will determine the industry price?
A report from the college dean indicates that for the previous semester, the grade distribution for the Department of Psychology included 135 As, 158 Bs, 140 Cs, 94 Ds, and 53 Fs. Determine what kind...
Grades in a statistics course and an operations research course taken simultaneously were as follows for a group of students. Are the grades in statistics and operations research related? Use a =...
An experiment with artillery shells yields the following data on the characteristics of lateral deflections and ranges. Would you conclude that deflection and range are independent? Use a = 0.05....
A study is being made of the failures of an electronic component. There are four types of failures possible and two mounting positions for the device. The following data have been taken: Would you...
What is the risk profile of your company? (How much overall risk is there in this firm? Where is this risk coming from (market, firm, industry or currency)? (APPLE COMPANY LATEST DATA) How is the...
What is the duration for the following bond with annual payments? 5.6300 5.7957 4.9894 5.1910 5.3806
DOLLAR TREE GROCERY OUTLET Short-Term Liquidity 2021 2022 2021 2022 Current Ratio 1.35 1.51 1.86 1.67 Quick Ratio 0.24 0.15 0.63 0.42 Cash Ratio Cash Conversion Cycle 34.78 45.75 19.41 21.61 Days...

Show that the Midpoint method and the Modified Euler method give the same approximations to the initial-value

Question:

Step by Step Answer:

The Modified Euler method and the Midpoint method give the same resul...View the full answer

Numerical Analysis

Students also viewed these Numerical Analysis questions