Purchase Solution

Gaussian Quadrature

Not what you're looking for?

Ask Custom Question

1. Consider approximating integrals of the form

I ( f ) = ∫ √x f(x)dx

in which f(x) has several continuous derivatives on [0, 1]
a. Find a formula

∫ √x f(x)dx ≈ w1 f(x1) ≡ I1( f )

which is exact if f(x) is any linear polynomial.

b. To find a formula

∫ √x f(x)dx ≈ w1 f(x1) + w2 f(x2) ≡ I2( f )

which is exact for all polynomial of degree ≤ 3, set up a system of four equations with unknown w1, w2, x1, x2 and find the values

Purchase this Solution
Solution Summary

This solution is comprised of a detailed explanation to answer Gaussian Quadrature problems.

Solution Preview

Solution:
We need to find two unknowns, the weight and the node ...

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Approximation o integral with Gaussian quadrature

    102207 Approximation of Two Integrals with Gaussian Quadrature Approximate the following integrals using Gaussian quadrature with n = 3 and n = 4 then compare your results to the exact values of the integrals.

  • Calculations with a Gaussian Quadrature

    477970 Calculations with a Gaussian Quadrature I need some help completing the following: Find the nodes x_i and the weights w_i so that the Gaussian quadrature of the sum from i=1 to 2 of (w_i) f(x_i) approximating the integral from -1 to 1 of f(

  • Legrende Polynomials, Gaussian Quadrature and Rodrigues Formula

    55876 Legrende Polynomials, Gaussian Quadrature and Rodrigues Formula Please see the attached file for the fully formatted problems. Please see the attached file for the complete solution. Thanks for using BrainMass.

  • Polynomials - Horner's Method, etc.

    Here xk* and ak* denote the Gaussian quadrature points ,and the appropriate summation weights. For the last question d) 2. I have posted a whole other thing on Gaussian Quadrature, if you'd like to read more.

  • Numerical integration using Simpson and Gaussian quadrature

    515319 Numerical integration using Simpson and Gaussian Quadrature With the specified accuracy integrate the function using Simpson's one-third rule and Gaussian quadrature: Int_0^3 Int_{-1}^2 Int_1^4 e^x y^3 z^2 dxdydz, where Int_a^b f(x)dx denotes

  • Numerical analysis and Gaussian quadrature

    Build a 25- point numerical integration scheme based on 5- point Gaussian quadrature in the x and y directions. Specify the quadrature points and the summation weights.

  • Quadrature

    28204 Mathematical Methods: Quadrature (a) Describe how the weights for the order 4 closed Newton-Cotes quadrature formula could be found. Do NOT calculate the weights.

  • Phasor Diagram for Synchronous Generator

    a) Draw a phasor diagram for this condition indicating the terminal voltage, armature current, location of direct and quadrature axes.

  • Deriving an integration rule

    38309 Deriving an integration rule Derive an integration rule for the domain [0,1] based on the quadrature points x1=0, x2=1/3 and x3=1, which is exact for polynomials of degree <= 2. Please see attached for full question.

View More Related Solutions