(c) We want to find a three-point formula, [*^* ƒ (x)dx = w₁ f(x1) + w2f (x2) + wzf(xx) + E, -h similar to the two-point formula in part ((b)). X1 < x2 < X3, (3) Definite integrals of f(x) and f(x) on a symmetric interval should be equal, i.e. L f(x)dx = L f(x)dx. -h (4) The quadrature rule should also possess such a property of integrals. Using this ar- gument of symmetry, show that x2 = 0 and find relations between x₁ and x3; and between w₁ and w3. Then, calculate the weights and points that make this rule ex- act for polynomials of the highest degree possible. Find the error term and write the quadrature formula (3).
(c) We want to find a three-point formula, [*^* ƒ (x)dx = w₁ f(x1) + w2f (x2) + wzf(xx) + E, -h similar to the two-point formula in part ((b)). X1 < x2 < X3, (3) Definite integrals of f(x) and f(x) on a symmetric interval should be equal, i.e. L f(x)dx = L f(x)dx. -h (4) The quadrature rule should also possess such a property of integrals. Using this ar- gument of symmetry, show that x2 = 0 and find relations between x₁ and x3; and between w₁ and w3. Then, calculate the weights and points that make this rule ex- act for polynomials of the highest degree possible. Find the error term and write the quadrature formula (3).
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
Related questions
Question
Transcribed Image Text:(c) We want to find a three-point formula,
[*^* ƒ (x)dx = w₁ f(x1) + w2f (x2) + wzf(xx) + E,
-h
similar to the two-point formula in part ((b)).
X1 < x2 < X3,
(3)
Definite integrals of f(x) and f(x) on a symmetric interval should be equal, i.e.
L
f(x)dx =
L
f(x)dx.
-h
(4)
The quadrature rule should also possess such a property of integrals. Using this ar-
gument of symmetry, show that x2 = 0 and find relations between x₁ and x3; and
between w₁ and w3. Then, calculate the weights and points that make this rule ex-
act for polynomials of the highest degree possible. Find the error term and write the
quadrature formula (3).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 1 steps with 3 images
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage