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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2018 • Question 4

Question

Math 6610 • Analysis of Numerical Methods I Spring 2018 • Question 4

Finite difference formulas

Given \(h>0\), compute weights \(w_j\) for the following 5-point finite difference formula for the third derivative \(f^{(3)}(x)\): \[ f^{(3)}(x)\approx \sum _{j=-2}^{2}w_j f(x+jh) \] \[ = w_{-2}f(x-2h)+w_{-1}f(x-h)+w_0f(x)+w_1f(x+h)+w_2f(x+2h). \] What is the order of accuracy of your formula?

Raw LaTeX

{Finite difference formulas}

Given \(h>0\), compute weights \(w_j\) for the following 5-point finite difference
formula for the third derivative \(f^{(3)}(x)\):
\[
  f^{(3)}(x)\approx \sum_{j=-2}^{2}w_j f(x+jh)
\]
\[
  =
  w_{-2}f(x-2h)+w_{-1}f(x-h)+w_0f(x)+w_1f(x+h)+w_2f(x+2h).
\]
What is the order of accuracy of your formula?

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Topic Tags

Finite Difference Boundary Value Problems Finite Difference Methods Linear Programming and Optimization Numerical Differentiation and Finite Difference Operators