Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 6.2, Problem 1E
Using initial condition
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
3.
Z
e2
n
dz, n = 1, 2,.
..
31.
On Feb. 8, this year, at 6am in the morning all UiB meteorology professors met to discuss a highly unfortunate
and top-urgent crisis: Their most precious instrument, responsible for measuring the air temperature hour-by-
hour, had failed - what if the Bergen public would find out? How would they plan their weekend without
up-to-date air temperature readings? Silent devastation - and maybe a hint of panic, also - hung in the room.
Apprentice Taylor, who - as always - was late to the meeting, sensed that this was his chance to shine! Could
they fake the data? At least for some hours (until the measurements would work again)? He used to spend a
lot of time online and thus knew the value of fake data, especially when it spread fast!
He reminded the crying professors of a prehistoric project with the title "Love your derivatives as you love
yourself!" - back then, they had installed top-modern technology that not only measured the air temperature
itself, but also its 1st, 2nd, 3rd, 4th, and…
Chapter 6 Solutions
Numerical Analysis
Ch. 6.1 - Show that the function y(t)=tsint is a solution of...Ch. 6.1 - Show that the function y(t)=esint is a solution of...Ch. 6.1 - Use separation of variables to find solutions of...Ch. 6.1 - Find the solutions of the IVP given by y(0)=0 and...Ch. 6.1 - Apply Eulers Method with step size h=1/4 to the...Ch. 6.1 - Apply Eulers Method with step size h=1/4 to the...Ch. 6.1 - (a) Show that y=tan(t+c) is a solution of the...Ch. 6.1 - (a) Show that y=tanh(t+c) is a solution of the...Ch. 6.1 - For which of these initial value problems on [0,...Ch. 6.1 - Sketch the slope field of the differential...
Ch. 6.1 - Find the solutions of the initial value problems...Ch. 6.1 - (a)Show that if a0, the solution of the initial...Ch. 6.1 - Use separation of variables to solve the initial...Ch. 6.1 - Find the solution of the initial value problem...Ch. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Apply Eulers Method with step size h=0.1 on [0, 1]...Ch. 6.1 - Plot the Eulers Method approximate solutions for...Ch. 6.1 - Plot the Eulers Method approximate solutions for...Ch. 6.1 - Prob. 4CPCh. 6.1 - For the IVPs in Exercise 4, make a log-log plot of...Ch. 6.1 - Prob. 6CPCh. 6.1 - Plot the Eulers Method approximate solution on [0,...Ch. 6.1 - Plot the Eulers Method approximate solution on [0,...Ch. 6.1 - Calculate the Eulers Method approximate solution...Ch. 6.1 - Calculate the Eulers Method approximate solution...Ch. 6.1 - Plot the Eulers Method approximate solution on [0,...Ch. 6.2 - Using initial condition y(0)=1 and step size...Ch. 6.2 - Using initial condition y(0)=0 and step size...Ch. 6.2 - Find the formula for the second-order Taylor...Ch. 6.2 - Apply the second-order Taylor Method to the...Ch. 6.2 - (a) Prove (6.22) (b) Prove (6.23).Ch. 6.2 - Apply the Explicit Trapezoid Method on a grid of...Ch. 6.2 - Prob. 2CPCh. 6.2 - Prob. 3CPCh. 6.2 - Prob. 4CPCh. 6.2 - Prob. 5CPCh. 6.2 - Plot the Trapezoid Method approximate solution on...Ch. 6.2 - Calculate the Trapezoid Method approximate...Ch. 6.2 - Calculate the Trapezoid Method approximate...Ch. 6.2 - Prob. 9CPCh. 6.3 - Apply the Eulers Method with step size h=1/4 to...Ch. 6.3 - Apply the Trapezoid Method with h=1/4 to the...Ch. 6.3 - Convert the higher-order ordinary differential...Ch. 6.3 - Apply the Trapezoid Method with h=1/4 to the...Ch. 6.3 - (a) Show that y(t)=(et+ett2)/21 is the solution of...Ch. 6.3 - Apply Eulers Method with step sizes h=0.1 and 0.01...Ch. 6.3 - Carry out Computer Problem 1for the Trapezoid...Ch. 6.3 - Prob. 3CPCh. 6.3 - Prob. 4CPCh. 6.3 - Prob. 5CPCh. 6.3 - Adapt pend.m to build a damped pendulum with...Ch. 6.3 - Prob. 7CPCh. 6.3 - Prob. 8CPCh. 6.3 - Prob. 9CPCh. 6.3 - Prob. 10CPCh. 6.3 - Prob. 11CPCh. 6.3 - Prob. 12CPCh. 6.3 - Prob. 13CPCh. 6.3 - Prob. 14CPCh. 6.3 - Prob. 15CPCh. 6.3 - A remarkable three-body figure-eight orbit was...Ch. 6.4 - Apply the Midpoint Method for the IVPs...Ch. 6.4 - Carry out the steps of Exercise 1 for the IVPs...Ch. 6.4 - Apply fourth-order Runge-Kutta Method to the IVPs...Ch. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Consider the initial value problem y=y . The...Ch. 6.4 - Prob. 7ECh. 6.4 - Prob. 1CPCh. 6.4 - Apply the fourth-order Runge-Kutta Method solution...Ch. 6.4 - Carry out the steps of Computer Problem 2, but...Ch. 6.4 - Prob. 4CPCh. 6.4 - Plot the fourth-order Runge-Kutta Method...Ch. 6.4 - Plot the fourth-order Runge-Kutta Method...Ch. 6.4 - Prob. 7CPCh. 6.4 - Prob. 8CPCh. 6.4 - Prob. 9CPCh. 6.4 - Prob. 10CPCh. 6.4 - Adapt the orbit .m MATLABs program to animate a...Ch. 6.4 - Assess the conditioning of the Lorenz equations by...Ch. 6.4 - Follow two trajectories of the Lorenz equations...Ch. 6.4 - Prob. 14CPCh. 6.4 - Prob. 15CPCh. 6.4 - Prob. 16CPCh. 6.4 - Prob. 17CPCh. 6.4 - Prob. 18CPCh. 6.4 - Run tacoma.m with wind speed W=80km/hr and initial...Ch. 6.4 - Replace the Trapezoid Method by fourth-order...Ch. 6.4 - The system is torsionally stable for W=50km/hr ....Ch. 6.4 - Find the minimum wind speed W for which a small...Ch. 6.4 - Prob. 5SACh. 6.4 - Prob. 6SACh. 6.4 - Prob. 7SACh. 6.5 - Write a MATLAB implementation of RK23 (Example...Ch. 6.5 - Prob. 2CPCh. 6.5 - Prob. 3CPCh. 6.5 - Compare the results of Computer Problem 3 with the...Ch. 6.5 - Apply a MATLAB implementation of RKF45 to...Ch. 6.6 - Using initial condition y(0)=0 and step size...Ch. 6.6 - Find all equilibrium solutions and the value of...Ch. 6.6 - Prob. 3ECh. 6.6 - Consider the linear differential equation y=ay+b...Ch. 6.6 - Apply Backward Euler, using Newtons Method as a...Ch. 6.6 - Carry out the steps in Computer Problem1 for the...Ch. 6.7 - Apply the Adams-Bashforth Two-Step Method to the...Ch. 6.7 - Carry out the steps of Exercise 1 on the IVPs...Ch. 6.7 - Prob. 3ECh. 6.7 - Prob. 4ECh. 6.7 - Show that the Implicit Trapezoid Method (6.89) is...Ch. 6.7 - Prob. 6ECh. 6.7 - Prob. 7ECh. 6.7 - Prob. 8ECh. 6.7 - Find the order and stability type for the...Ch. 6.7 - Prob. 10ECh. 6.7 - Prob. 11ECh. 6.7 - The Mime-Simpson Method is a weakly stable...Ch. 6.7 - Prob. 13ECh. 6.7 - (a) Use the matrix formulation to find the...Ch. 6.7 - Prob. 15ECh. 6.7 - (a) Use the matrix formulation to find the...Ch. 6.7 - Adapt the exmultistep.m program to apply the...Ch. 6.7 - Adapt the exmultistep.m program to apply the...Ch. 6.7 - Prob. 3CPCh. 6.7 - Prob. 4CPCh. 6.7 - Prob. 5CPCh. 6.7 - Prob. 6CPCh. 6.7 - Prob. 7CPCh. 6.7 - Prob. 8CPCh. 6.7 - Prob. 9CPCh. 6.7 - Change Program 6.8 into a fourth-order...
Additional Math Textbook Solutions
Find more solutions based on key concepts
1. How much money is Joe earning when he’s 30?
Pathways To Math Literacy (looseleaf)
147. Draining a tank Water drains from the conical tank shown in the accompanying figure at the rate .
a. What...
University Calculus
Silvia wants to mix a 40% apple juice drink with pure apple juice to make 2 L of a juice drink that is 80% appl...
Beginning and Intermediate Algebra
(a) Make a stem-and-leaf plot for these 24 observations on the number of customers who used a down-town CitiBan...
APPLIED STAT.IN BUS.+ECONOMICS
For each hour of class time, how many hours outside of class are recommended for studying and doing homework?
Elementary Algebra For College Students (10th Edition)
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
- Consider a forest where the population of a particular plant species grows exponentially. In a real-world scenario, we often deal with systems where the analytical function describing the phenomenon is not available. In such cases, numerical methods come in handy. For the sake of this task, however, you are provided with an analytical function so that you can compare the results of the numerical methods to some ground truth. The population P(t) of the plants at time t (in years) is given by the equation: P(t) = 200 0.03 t You are tasked with estimating the rate of change of the plant population at t = 5 years using numerical differentiation methods. First, compute the value of P'(t) at t = 5 analytically. Then, estimate P'(t) at t = 5 years using the following numerical differentiation methods: ⚫ forward difference method (2nd-order accurate) 3 ⚫ backward difference method (2nd-order accurate) ⚫ central difference method (2nd-order accurate) Use h = 0.5 as the step size and round all…arrow_forwardQ/ By using polar Coordinates show that the system below has a limit cycle and show the stability of + his limit cycle: X² = x + x(x² + y² -1) y* = −x + y (x² + y²-1) -xarrow_forwardxy Q/Given H (X,Y) = ex-XX+1 be a first integral find the corresponding system and study the Stability of of critical point of this system.arrow_forward
- Q/ show that H (X,Y) = x²-4x-x² is 2 first integral of the system Y° = y 0 y° = 2x + x 3 then study the stability of critical point and draw phase portrait.arrow_forwardQ/Given the function H (X,Y) = H (X,Y) = y 2 X2 2 2 ²** 3 as a first integral, find the correspoding for this function and draw the phase portrait-arrow_forwardQ/ show that the system has alimit cycle and draw phase portrait x = y + x ( 2-x²-y²)/(x² + y²) ½ 2 y = -x+y ( 2-x² - y²) / (x² + y²) ½/2arrow_forward
- Let (x,y)~f(x,y) = x(x-1)! (x-y)! 0; y = x,... x = 0,1,..., y 1- Show that whether x and y are indep. or not? 2- p(x = y) e.w. مسلم مجید Muslim mathsarrow_forwardA sequence X = (xn) is said to be a contractive sequence if there is a constant 0 < C < 1 so that for all n = N. - |Xn+1 − xn| ≤ C|Xn — Xn−1| -arrow_forwardPlease explain this theorem and proofarrow_forward
- Please answer number 17arrow_forwardNicole organized a new corporation. The corporation began business on April 1 of year 1. She made the following expenditures associated with getting the corporation started: Expense Date Amount Attorney fees for articles of incorporation February 10 $ 40,500 March 1-March 30 wages March 30 6,550 March 1-March 30 rent Stock issuance costs March 30 2,850 April 1-May 30 wages Note: Leave no answer blank. Enter zero if applicable. April 1 May 30 24,000 16,375 c. What amount can the corporation deduct as amortization expense for the organizational expenditures and for the start-up costs for year 1 [not including the amount determined in part (b)]? Note: Round intermediate calculations to 2 decimal places and final answer to the nearest whole dollar amount. Start-up costs amortized Organizational expenditures amortizedarrow_forward3) Find the surface area of z -1≤ y ≤1 = 1 + x + y + x² over the rectangle -2 ≤ x ≤ 1 andarrow_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