Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 6.4, Problem 18CP
a.
To determine
To plot the trajectory with initial conditions for a three-body orbit problem using Runge- kutta order4 method.
b.
To determine
To plot the trajectory with initial conditions for a three body orbitusing Runge- kutta order4 method.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Problem. 9: Let z = x?
7 xy + 6 y? and suppose that (x, y) changes from (2, 1) to (1.95, 1.05 ). (Round your answers to four decimal places.)
(a) Compute Az.
(b) Compute dz.
?
West Gorham High School is to be located at the population center of gravity of three communities: Westbrook,
population 17,500, Scarborough, population 23,000, and Gorham, population 33,500. Westbrook is located at
43.6769°N, 70.3717°W, Scarborough is located at 43.5781°N, 70.3222°W, and Gorham is located at 43.6795°N,
70.4447°W.
a. Where should West Gorham High School be located?
West Gorham High School be located at °N, W. (Enter your responses rounded to four decimal places.)
With reference to the attached scenario and questions:
The 100 meter diameter wheel needs to be designed so that it rotates at a constant rate and every complete revolution takes 15 minutes. The wheel has been installed in a vertical plane and the lowest seat is 2m above the ground surface. Each ride consists of only one full rotation.
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...
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
- Construct a model for the number of cats, y, after x months that make use of the following assumptions: 1. It begins with two cats – one female and one male, both unneutered. 2. Each litter is composed of 4 kittens – 3 males and 1 female. 3. It takes four months before a new generation of cats is born. 4. No cat dies (all are healthy) and no new cats are introduced.arrow_forwardFrom riding the Ferris wheel, you observe the following: (1) The gondola is 2 meters off the ground; (2) The top portion of the wheel is 60 meters from the gondola at the base (3) You have reached the top of the wheel after 5 minutes; (4) You reach the base again at exactly after 10 minutes; and (5) The wheel rotates 3 times until it stopped. From these observations, execute the task given and please be guided by the procedure shown below in sketching the graph. Let y be the height of the Ferris wheel in meters (m) and x be the time in minutes (min)arrow_forwardster Com... sin(-3pi/2 McGraw-Hill Conn.. MywCC Q Chapter 1 Flashca... 6 / 6 100% (y+2)2 = 1. x2 16. Find the center, vertices, and foci of the ellipse given by the equation 16 49 14,588 1 37 Ps MacBook Pro Display Connected: Mirror Displays Extend Desktop & 4 5 7 8arrow_forward
- 3. Find the orthogonal trajectory of y =c cos xarrow_forwardIn each of Problems 1 through 5, determine the canonical form of the elliptic equation. 1. uzz + 2uzy + 5uyy + uy = 0 2. 3uzz - 2uzy + 2uyy = 0arrow_forward11.6: Problem 7 Find the point on the graph of z 3x2 + 2y at which vector (24, 8, 2) is normal to the tangent plane. n = ||arrow_forward
- 12. Do the data in the accompanying table support Kepler's third law? Give reasons for your answer. Semimajor axis a (101º m) Planet Period T (years) Mercury 5.79 0.241 Venus 10.81 0.615 Mars 22.78 1.881 Saturn 142.70 29.457arrow_forwardProblem 2: (a) Consider a right circular cylinder of radius R centered on the z axis. Find the relation betweenpand z that describes the geodesics (stationary paths) on the surface of this cylinder. (b) Specifically, for an initial point at (p, z) = (0,0) and an endpoint at arbitrary (pf, zf), write down an equation for the stationary paths between these two points. [There are many such paths. Why?]arrow_forwardS Module 5 Part 3 Desmos | School X Module 5 part 3 9 Launch Meeting - Zoom + com/activitybuilder/student/601be852346f470468897058#screenldx=51 Problem 1 In order to show that AFGH is congruent to AFG'H', how many degrees must AFGH be rotated clockwise about the origin? 10y O 90° O 180° 41 O 270° 2 O 360° -10 -8 -6 -4-2 2. 4 S 10 -2 G' -4 -6 -8 -10arrow_forward
- QUESTION 1 City hall wishes to learn about the rate of parking meter use. They choose 8 downtown blocks at random (these are city blocks, not statistical blocks!), and on each block they choose 5 meters at random. Six weeks are chosen randomly from the year, and the usage (money collected) on each meter is measured every day (Monday through Sunday) for all the meters on those weeks. a) Write out an appropriate linear model. id df only) for this design.arrow_forwardSuppose a planet is found with an orbital period of 63.00 years. (Round the final answer to three decimal places.) 1. Its distance can be estimated using Kepler's third law. True 2. If its orbit is circular, what is the orbit's radius? Express your answer in AU.arrow_forwardIf two objects travel through space along two different curves, it is often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) Their paths might intersect, but we need to know whether the objects are in the same position at the same time. Suppose two particles travel along the following space curves. r,(t) = (t, t, t³), r,(t) = (1 + 6t, 1 + 30t, 1 + 126t) for t 2 0 Find the points at which their paths intersect. (If an answer does not exist, enter DNE.) smaller x-value (х, у, 2) larger x-value (х, у, 2) Find the time(s) when the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) t =arrow_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
What is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY