+1-415-670-9189
info@expertsmind.com
Find the constants of the quadrature rule
Course:- Mathematics
Reference No.:- EM132308112




Assignment Help
Expertsmind Rated 4.9 / 5 based on 47215 reviews.
Review Site
Assignment Help >> Mathematics

Assignment - Final Exam

Problem 1 - Suppose that

limh→0 f(h) = M, and M = f(h) + K1h2 + K2h4 + K3h6 + · · ·

Find a combination of f(h) and f(h/2) that is a better estimate of M.

Problem 2 - Using the data f(x - h), f(x), f(x + 2h) construct the best possible approximation of f'(x). Also, find the order of a truncation error O(hp).

Problem 3 - Consider the following integral

02ex^2 dx.

(a) Use the Composite Trapezoidal rule to find approximations with n = 1, 2, 4.

(b) Use Romberg integration to compute R3,3. (Hint: use previously obtained approximation).

Problem 4 - Consider the integral

0π/4 ln(cos(x)) dx.

(a) Use Gaussian quadrature with n = 3 to approximate the integral.

(b) Use the Composite Simpson's rule with n = 4 to approximate the integral.

Problem 5 - Consider the following improper integral.

01 sin(x)/x¼ dx

Use composite Simpson's rule with n = 4 to approximate the improper integral.

Problem 6 - Find the constants a, b, c, of the following quadrature rule.

-11 f(x)dx = af(-1) + bf(1) + cf'(-1),

that has degree of precision 2. (Hint: the integration must be exact for any polynomial function with degree up to 2)

Problem 7 - Consider the following initial value problem

y'= ty + 1, 1 ≤ t ≤ 2, y(1) = 2, with h = 0.1

(a) Prove that the initial value problem has a unique solution on t ∈ [1, 2] and y ∈ (-∞, ∞).

(b) Use the Modified Euler method to approximate w1.

(c) Starting values from Modified Euler method, use Adams-Moulton Two-Step Implicit method to find w2, w3.




Put your comment
 
View Conversion
Minimize
  1. user image
    len2308112

    This exam contains 10 pages (including this cover page) and 7 problems. Check to see if any pages are missing. Enter all requested information on the top of this page, and put your initials on the top of every page, in case the pages become separated. You may use any calculator on this exam. You are required to show your work on each problem on this exam.



Ask Question & Get Answers from Experts
Browse some more (Mathematics) Materials
The line y = 0.15x + 0.79 represents an estimate of the average cost of gasoline each year. The line 0.11x -y =-0.85 estimates the price of gasoline in January of each year.
A cheetah spots a gazelle 132 meters away. The cheetah starts towards the gazelle at a speed of 18 meters per second. At the same instant, the gazelle starts moving away at
The cost of one lunch ticket is $2.25. What is the equation the student could use to calculate the amount of money, m, left after d days, assuming the student uses one lunch
Draw a graph of the equation y = x(1 - x) for x between 0 and 1. What is the maximum value of y? Why does this show that the variance (see Problem 10 in this section) of the
Mack-son and Jim works in the same office. At any particular time during office hours, the probability that Mack-son is in the office is 0.7 and probability that Jim is in t
"You are asked to create an 8-character password, and each character may be any of the 26 letters of the alphabet or the 9 numerals 1 through 9. How many different passwords
Calculate the directional derivative of f(x,y) = x2/3 + y2/3 at the point (1,2) in the direction of v ≤ -3, 5. Calculate the directional derivative of g(x,y) = ln(x + ey) at t
A rancher has 1200m of fencing to enclose 2 rectangular corrals. The corrals have the same dimensions and one side in common. What dimensions will maximize the enclosed area