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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2021 • Question 3

Question

Math 6610 • Analysis of Numerical Methods I Fall 2021 • Question 3

(Finite difference formulas) Given \(h > 0\), compute weights \(\{w_j\}_{j=0}^2\) for the following one-sided finite difference formula for the first derivative \(f'(x)\): \[ f'(x) \approx \sum _{j=0}^2 w_j f(x+jh) = w_0 f(x) + w_1 f(x+h) + w_2 f(x+2h). \]

What is the order of accuracy of your formula?

Raw LaTeX

(Finite difference formulas)
Given \(h > 0\), compute weights \(\{w_j\}_{j=0}^2\) for the following one-sided finite difference formula
for the first derivative \(f'(x)\):
\[
f'(x) \approx \sum_{j=0}^2 w_j f(x+jh)
= w_0 f(x) + w_1 f(x+h) + w_2 f(x+2h).
\]


What is the order of accuracy of your formula?

Topic Tags

Finite Difference Methods Linear Programming and Optimization