Numerical Differentiation

Abstract

For more complex problems analytical derivatives are not always available and have to be approximated by numerical methods, for instance, to calculate forces from a complicated force field. The simplest method is the explicit forward difference quotient which has a very poor error order. Precision can be improved significantly by using a symmetric difference quotient. Higher order methods are introduced which can be systematically generated with the Romberg extrapolation method. A computer experiment compares the precision of methods with different error orders. Higher derivatives and differential operators in more dimensions can be obtained from polynomial interpolation.