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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2018 • Question 3

Question

Math 6610 • Analysis of Numerical Methods I Fall 2018 • Question 3

Finite difference formulas

Given \(h>0\), compute weights \(v_0\) and \(\{w_j\}_{j=-1}^{1}\) for the following finite difference formula for the third derivative \(f^{(3)}(x)\): \[ f^{(3)}(x)\approx v_0f'(x)+\sum _{j=-1}^{1}w_j f(x+jh) \] \[ =v_0f'(x)+w_{-1}f(x-h)+w_0f(x)+w_1f(x+h). \] What is the order of accuracy of your formula?

Raw LaTeX

{Finite difference formulas}

Given \(h>0\), compute weights \(v_0\) and \(\{w_j\}_{j=-1}^{1}\) for the following
finite difference formula for the third derivative \(f^{(3)}(x)\):
\[
  f^{(3)}(x)\approx v_0f'(x)+\sum_{j=-1}^{1}w_j f(x+jh)
\]
\[
  =v_0f'(x)+w_{-1}f(x-h)+w_0f(x)+w_1f(x+h).
\]
What is the order of accuracy of your formula?

Topic Tags

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