Lecture 12

Outline for "Computational Methods", Lecture 12: Numerical Differentiation

DERIVATION OF DIFFERENCE APPROXIMATIONS USING UNDETERMINED COEFFICIENTS

  1. Forward 2nd order accurate approximation to the first derivative
  2. Forward 1st order accurate approximation to the second derivative
  3. Skewed 4th order accurate approximation to the second derivative

NUMERICAL DIFFERENTIATION USING DIFFERENCE OPERATORS

  1. Difference Operators
    1. 1st order difference operators
    2. Notes
    3. 2nd order forward difference operator
    4. 3rd order backward difference operator
    5. 2nd order central difference operator 
    6. 2nd order mixed difference operator
  2. Approximation to Differentiation Using Difference Operators
    1. 1st order backward difference operator approximation to the first derivative
    2. 1st order central difference operator approximation to the first derivative
    3. Central difference approximation to the first derivative as an average of 1st order forward and backward difference approximations
    4. General difference operator approximations to derivatives
Citation: Westerink, J. (2011, January 12). Lecture 12. Retrieved June 19, 2013, from Notre Dame OpenCourseWare Web site: http://ocw.nd.edu/civil-engineering-and-geological-sciences/computational-methods/lectures/lecture-12.
Copyright 2012, by the Contributing Authors. This work is licensed under a Creative Commons License. Creative Commons License