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Computer Physics Communications 161 (2004) 109118 www.elsevier.com/locate/cpc

Summary: Computer Physics Communications 161 (2004) 109­118
On the use of higher-order formula for numerical derivatives
in scientific computing
N. Mohankumar a,c,
, Scott M. Auerbach a,b
a Department of Chemistry, University of Massachusetts, Amherst, MA 01003, USA
b Department of Chemical Engineering, University of Massachusetts, Amherst, MA 01003, USA
c Radiological Safety Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India
Received 17 November 2003; accepted 15 February 2004
Available online 2 July 2004
In many situations, the numerical derivative of a function at a point x must be calculated since the function is not defined by a
closed-form expression, but rather by values of the function at grid points at and around x. This typically arises when enforcing
the boundary conditions while solving a differential equation. Usually, one employs a 2- or 3-point formula to approximate the
derivative. On the other hand, the use of a higher-order formula, such as a 7- or even a 10-point approximation, based on the
method of undetermined coefficients, can sometimes lead to better accuracy and enhanced computational efficiency. We show
that significant improvements arise from using higher-order formulas for the first derivative in two important problems: the
calculation of quantum mechanical reaction rates using the Miller­Schwartz­Tromp correlation function, and the calculation of
the radioactivity migration in a porous medium.


Source: Auerbach, Scott M. - Department of Chemistry, University of Massachusetts at Amherst


Collections: Chemistry