DIFF EQUAT W/BOUNDAR >PRINT UPGRADE<
9th Edition
ISBN: 9781337810906
Author: ZILL
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 9.2, Problem 16E
Consider the initial-value problem y′ = 2y, y(0) = 1. The analytic solution is y(x) = e2x.
- (a) Approximate y(0.1) using one step and the RK4 method.
- (b) Find a bound for the local truncation error in y1.
- (c) Compare the error in y1 with your error bound.
- (d) Approximate y(0.1) using two steps and the RK4 method.
- (e) Verify that the global truncation error for the RK4 method is O(h4) by comparing the errors in parts (a) and (d).
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
MATLAB. Awnser the * parts in the comments
Matlab. Awnser the * questions in the comments of the code.
Matlab. Awnser the * parts in the comments of the code.
Chapter 9 Solutions
DIFF EQUAT W/BOUNDAR >PRINT UPGRADE<
Ch. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Consider the initial-value problem y = 2x 3y + 1,...Ch. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Repeat Problem 19 using the improved Euler’s...Ch. 9.1 - Prob. 21ECh. 9.2 - Use the RK4 method with h = 0.1 to approximate...Ch. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Consider the initial-value problem y′ = 2y, y(0) =...Ch. 9.2 - Prob. 17ECh. 9.2 - Consider the initial-value problem y′ = 2x – 3y +...Ch. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.3 - Prob. 1ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.4 - Use Euler’s method to approximate y(0.2), where...Ch. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - In Problems 1-18 use Definition 7.1.1 to find ℒ{f...Ch. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - The electrostatic potential u between two...Ch. 9.5 - Consider the boundary-value problem y″ + xy = 0,...Ch. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - In Problems 1–4 construct a table comparing the...Ch. 9 - In Problems 1–4 construct a table comparing the...Ch. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Matlab. Add the awnsers for the * questions in the code comments.arrow_forward4. Suppose f A → B is a bijection. Prove that f-1: BA is a bijection.arrow_forwardProve by mathematical induction that for any positive integer n, the sum of the cubes of the first n natural numbers is given by: n Σκ k=1 (n(n + 1))²arrow_forward
- 1 L'Ina (ln x) 2020 dx 0arrow_forwardCalibri BIUAAAA ויו Text in Italian is not being checked. Do you want to add it as a proofing language? Task 12 Fig 1 75 75 75 Fig 2 Fig 3j Add Figures 1 to 3 each shows a top view and a front view of models. Make use of the lineated paper for isometric projection and take each block on the paper as being 10mm x 10mm. Use the indicated sizes and draw an isometric view of each of the three models Samsung Galaxy A04earrow_forwarda) show that the empty set and sigletonset are convex set. 6) show that every sub space of linear space X is convex but the convers heed not be true. c) let Mand N be two convex set of a linear Space X and KEF Show that MUN is conevex and (ii) M-N is convex or hot A and is MSN or NSM show that MUN convex or not, 385arrow_forward
- xp x+xarrow_forwardFor the given graph, determine the following. -3 12 УА 4 3 - -1 ° 1 2 3 x -1. -2- a. Determine for which values of a the lim f (x) exists but f is not continuous at x = a. a b. Determine for which values of a the function is continuous but not differentiable at x = a. aarrow_forwardI write with prove one-to-one linear Sanction but not onto Lexample.) b) write with Prove on to linear function but not oh-to-on (example). c) write with prove example x=y St Xandy two linear space over Sielad F.arrow_forward
- Use the following graph of ƒ (x) to evaluate ƒ' (−1) and ƒ' (2). y +10+ 9 8 7 6 5 4 3 2 1- -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 x 3 4 0 8 9 10 -2 3 -4 5 -6 -7 -8 -9 -10- f'(-1)= f' (2)arrow_forwardFor the following function f and real number a, a. find the slope of the tangent line mtan = = f' (a), and b. find the equation of the tangent line to f at x = a. f(x) = 2 = ;a=2 a. Slope: b. Equation of tangent line: yarrow_forwardFor the following function f and real number a, a. find the slope of the tangent line mtan = f' (a), and b. find the equation of the tangent line to f at x = a. f(x) = 2x² + 3x; a = 2 a. Slope: b. Equation of tangent line: yarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY