Numerical Methods/Numerical Differentiation

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Often in Physics or Engineering it is necessary to use a calculus operation known as differentiation. Unlike textbook mathematics, the differentiated functions are data generated by an experiment or a computer code.

Begin with the Taylor series as seen in Equation 1.

Next by cutting off the Taylor series after the fourth term and evaluating it at h and -h yields Equations (2) and (3).

Then by subtracting Equation (2) by Equation (3) yields.

Central Difference[edit | edit source]

Forward Difference[edit | edit source]

Backward Difference[edit | edit source]

Second Derivative[edit | edit source]

The second order derivatives can be obtained by adding equations (2) and (3) (if properly expanded to include the fourth-derivative-term):

High Order Derivatives[edit | edit source]