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

DERIVATION OF DIFFERENCE APPROXIMATIONS USING UNDETERMINED COEFFICIENTS

*Forward 2*^{nd}order accurate approximation to the first derivative*Forward 1*^{st}order accurate approximation to the second derivative*Skewed 4*^{th}order accurate approximation to the second derivative

NUMERICAL DIFFERENTIATION USING DIFFERENCE OPERATORS

- Difference Operators
*1*^{st}order difference operators*Notes**2*^{nd}order forward difference operator*3rd order backward difference operato*r*2*^{nd}order central difference operator*2*^{nd}order mixed difference operator- Approximation to Differentiation Using Difference Operators
*1*^{st}order backward difference operator approximation to the first derivative*1*^{st}order central difference operator approximation to the first derivative*Central difference approximation to the first derivative as an average of**1*order forward and backward difference approximations^{st}*General difference operator approximations to derivatives*

Citation: Westerink, J. (2011, January 12). Lecture 12. Retrieved September 21, 2014, from Notre Dame OpenCourseWare Web site: http://ocw.nd.edu/civil-engineering-and-geological-sciences/computational-methods/lectures/lecture-12.

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