Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Math Expert


Home >> Math

problem: The backwards Euler difference 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 difference operator is consistent.
problem: Consider the Van der Pol oscillator

x′′ − µ(1 − x2)x′+ x = 0

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

(b) Taking µ = 2, use MatLab’s routine ode45 to compute the solution for the 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) What is the fixed point of the system? Use your numerical results to argue what the long time behavior of the system is.

problem: Consider the differential equation give by:

y′ = −10(y − sin t)

(a) 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.
describe why this verifies your scheme is convergent to order 1.

Math, Academics

  • Category:- Math
  • Reference No.:- M9170

Have any Question? 


Related Questions in Math

T angle between two forces of 37 n newtons and 55 n is

The angle between two forces of 37 N (Newtons) and 55 N is 36°. Find the magnitude of the resultant force. Do not round until the final answer. Then round to the nearest integer as needed.)

1 list and describe common steps in the evaluation of

1. List and describe common steps in the evaluation of vendor proposals. Construct a checklist with support for each item that you have included. 2. Why do companies use Service-Level Agreements (SLAs)? Give your answer ...

The polynomial gx-006x4nbsp140x3-53x2179xnbspmeasures the

The polynomial G(x)=-.006x 4  +.140x 3 -.53x 2 +1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase between 10 and 11 seconds?

1 discuss the difference between fairness and justice

1. Discuss the difference between "fairness" and "justice"? Should stakeholders be treated "fairly" or "justly"? Discuss. 2. Research Milton Friedman's view of corporate social responsibility. Should corporations adopt a ...

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 ...

Atmospheric pressure decreases by about 116 for every 1000

Atmospheric pressure decreases by about 11.6% for every 1000 meters you climb. The pressure at sea level is 1013 millibars (a unit of pressure). Construct an exponential model to represent the atmospheric pressure at a g ...

During most of the 20th century the united states was

During most of the 20th Century, the United States was clearly recognized as an innovation leader with an emphasis on technological innovation. Has that changed in the 21st Century? Have other countries begun to overtake ...

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?

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 ...

A set solution concept for a family of bargaining games f

A set solution concept for a family of bargaining games F is a function ? associating every bargaining game (S, d) in F with a subset of S (which may contain more than a single point). Let f : R4 → R be a function. Defin ...

  • 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