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

Find the area and the circumference of a circle with

Find the area and the circumference of a circle with diameter4m. Use the value 3.14 for π, and do not round your answers. Be sure to include the correct units in your answers.

An ethical analysis about philip morriss dont be maybe be

An ethical analysis about Philip Morris's "Don't be maybe, Be Marlboro" marketing campaign . You should analyse in terms of Stakeholder Analysis, Caroll's Pyramid, Utilitarianism, Deontology and Virtue Ethics. Most impor ...

The given angle is approximate find the value of the given

The given angle is approximate. Find the value of the given trigonometric function by finding the reference angle and attaching the proper sign sec 495.51 degrees (Round to three decimal places as needed.)

A principal of 4900 is invested at 775 interest compounded

A principal of $4900 is invested at 7.75% interest, compounded annually. How much will the investment be worth after 8 years? Use the calculator provided and round your answer to the nearest dollar.

Find the standard form other equation of the hyperbola find

Find the standard form other equation of the hyperbola. Find the center, vertices, foci, and asymptotes of the hyperbola. Sketch the hyperbola.  9y^2 - x^2 + 2x + 54y + 62 = 0

In a 150-300 word post discuss ways leaders and managers

In a 150-300 word post, discuss ways leaders and managers can create a servant leadership mentality in an organization. What are the pros and cons of servant leadership? Resources Textbook: Leading Change in your World T ...

Define the number of all the arrangements of 8 objects

Define the number of all the arrangements of 8 objects choosing 2 at a time without repetition. A. Order is important. (permutations). B. Order is not important (combinations). Please show problem worked out

The time it takes you to get to campus varies inversely as

The time it takes you to get to campus varies inversely as your driving rate. Averaging 20 miles per hour in terrible traffic, it takes you 1.5 hrs to get to campus. How long would the trip take averaging 60 miles per ho ...

You can win lolitas deep-6 lottery jackpot if you correctly

You can win Lolita's "Deep-6" lottery jackpot if you correctly choose 6 non-repeating integer numbers between 1 and 36 (in any order) and those numbers are drawn. You buy one ticket. What is the probability that it's the ...

The jurassic zoo charges 12for each adult admission and

The Jurassic Zoo charges $12for each adult admission and $2for each child. The total bill for the 259 people from a school trip was $1128. How many adults and how many children went to the zoo?

  • 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

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

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen