Purchase Solution

Numerical analysis and Gaussian quadrature

Not what you're looking for?

Ask Custom Question

A function of two variables f(x,y) is integrated over the square [0,2] x [-1,1]. ex: integral from 0 to 2 , integral from -1 to 1 f(x,y) dx dy. (I wanted to input integral symbols there but didn't know how). 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.

Note: f(x,y) is not given meaning it may be any function of 2 variables over the square [0,2] x [-1,1]

Purchase this Solution
Solution Summary

This solution answers questions involving numerical analysis and Guassian quadratures. Step by step calculations are provided.

Solution Preview

The last equation I = sum(sum( wi*wj*f(zi,nj+1) ) ) from i = 1,n; j = 1,n is the 25 point numerical integration scheme. It is derived and it states that we can integrate a function by using 25 points. These points are attained when we expand this sum. In this problem, n = 5. We can get the first five points for when i = 1.

i = 1:
I1 = ...

Purchase this Solution
Free BrainMass Quizzes
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.

Probability Quiz

Some questions on probability

Graphs and Functions

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

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

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.

  • Numerical integration using Simpson and Gaussian quadrature

    With specified accuracy, a numerical integration is performed using Simpson's rule and Gaussian quadrature.

  • 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.

  • 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

    Legrende Polynomials, Gaussian Quadrature and Rodrigues Formula are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

  • Gaussian Quadrature

    37586 Gaussian Quadrature 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.

  • Elementary Numerical Analysis : Gaussian Numerical Integration

    37558 Elementary Numerical Analysis : Gaussian Numerical Integration 1.

  • GAUSSIAN NUMERICAL INTEGRATION

    37559 Elementary Numerical Analysis GAUSSIAN NUMERICAL INTEGRATION 1. Consider approximating integrals of the form... in which f(x) has several continuous derivatives on [0, 1] a.

  • Quadrature (Matlab) Intergral Evaluated Forms

    Below is a naive implementation of an adaptive version of forward Euler quadrature. The program checks the if the tolerance TOL is met and recursively performs divide and conquer if it is not.

View More Related Solutions