Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Math Expert


Home >> Math

Instructions for computer part:

• The grader must be able to run one script, or one script for every problem and obtain the desired outcome (graphs, printed values, ect. . . ).
• Please be sure the filename is of the form “last name” then an “underscore” followed through the “problem set number” (and problem number if multiple files).

For illustration Newhall_HW9.m would include all answers generated by one file while Newhall_HW9_2.m would only have problem 2 within the script.

• Be sure to also comprise any files containing functions you have written.
• Please also comprise your last name in subject line.

The written parts must be turned in as usual on paper.

1. (20pts) (written) The backwards Euler different operator is given by
Nhyn = yn − yn−1/ hn − f(tn, yn)

For differential equation y′= f(t, y). Determine the order of the local truncation error. describe why this diference operator is consistent.

2. (40pts) consider the Van der Pol oscillator
x′′− µ(1 − x2)x′+ x = 0

(a) (Written) prepare this equation as a system of first order equations

(b) Taking µ = 2, use MatLab’s routine ode45 to find out the solution for initial value problem x(0) = 0 and x′(0) = 5 from t = 0 to t = 40. Plot x as a function of t and also plot x vs x′ in phase-space.

(c) Repeat for the initial conditions x(0) = 0 and x′ (0) = 0.01.

(d) (Written) what is the fixed point of the system? Use your numerical results to argue what the long time behavior of the system is.

3. (40pts) Consider the differential equation give by
y′= −10(y − sin t)

(a) (Written) Derive by hand exact solution that satisfies the initial condition
y(0) = 1.

(b) Numerically obtain the solution to the IVP using Forward Euler with a step size of h = 0.1 from t = 0 to t = 3. Print the value of the approximate solution at time t = 3. Also plot the exact solution (with a solid line) and the approximate solution (with square markers) on the same plot.

(c) Numerically determine the relative global error,
eh = |1 − yh(3)/y(3)|

Of your approximate solution at t = 3 when h = h, h/2, h/4, h/8 and h/16.
Plot the log of the relative error vs. the log of the spacing h. (written)
describe why this verifies your scheme is convergent to order 1.

Math, Academics

  • Category:- Math
  • Reference No.:- M9815

Have any Question? 


Related Questions in Math

A 500 8 bond is purchased on february 1 2004 to yield

A $500, 8% bond is purchased on February 1, 2004, to yield 10%compounded semi-annually. The interest on the bond is payable onFebruary 1 and August 1 each year. Find the purchase price if the bondis redeemable at face va ...

Consider an aumann model of incomplete information in which

Consider an Aumann model of incomplete information in which N = {I, II}, Y = {1, 2, 3, 4, 5, 6, 7, 8, 9}, FI = {{1},{2, 3},{4, 5},{6},{7},{8, 9}}, and FII = {{1},{2, 5},{3},{4, 7},{6, 9},{8}}. What are the connected comp ...

Trigonometry and calculusquestions 1-20 select the one best

Trigonometry and Calculus Questions 1-20: Select the one best answer to each question. 1. As a lumberjack, you attach a 50-foot wire from the top of a lean¬ing pine tree to a stake in the ground, forming a 70 degree angl ...

Al was an attorney in a small town and was very well

Al was an attorney in a small town and was very well respected. A couple retained Al to represent them on the purchase of a home. Before closing, Al informed the couple of payments that they were required to make by chec ...

Use the simplex method to maximize p 8x9y subject to 3x2y

Use the simplex method to maximize P= 8x+9y subject to 3x+2y is less than or equal to 12 6x+1y is less than or equal to 15 X is greater than 0 Y is greater than 0

According to a national poll of 375 college students 62

According to a national poll of 375 college students, 62% play video games more than 6 hours a week. Find the margin of error and the 95% confidence interval for the survey. Give your answers as percentages rounded to th ...

The material-handling systems for the maltese distribution

The material-handling systems for the Maltese distribution centre in La Valletta of Ekom makes use of hand transpallet trucks which can hold at most three roll containers, with a capacity of 15 packages each. Last Januar ...

In 450 words with referencesdiscuss why productivity is

In 450 words with references: Discuss why productivity is important, particularly in a healthcare organization. How do staffing models and labor optimization algorithms contribute towards productivity? During project man ...

1 given the following augmented matrix which represents a

1. Given the following augmented matrix which represents a linear system, solve the linear system for x, y, and z. If there is an infinite number of solutions then express the solutions in terms of z as the parameter. If ...

John borrowed 4700 from the bank in order to buy a new

John borrowed $4700 from the bank in order to buy a new piano. He will pay it off by equal payments at the end of each week for 3 years. The annual interest rate is 3.75%. Determine the size of payments, and the total in ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro