论文信息 - Some comments on the use of higher-order formula for numerical derivatives in scientific computing

Some comments on the use of higher-order formula for numerical derivatives in scientific computing

In an earlier article, we had indicated two applications where there was a significant improvement in accuracy due to the use of higher order approximation for certain spatial derivatives. The method of undetermined coefficients was used for this derivative approximation. In this note which is a sequel to the previous work, we provide a simple prescription for fixing the order of approximation of the required derivative. This procedure is based on the comparison of the various errors of the discretization process.

N. Mohankumar | Scott M. Auerbach

[1] Tucker Carrington,et al. A general framework for discrete variable representation basis sets , 2002 .

[2] H. M. Antia. Numerical Methods for Scientists and Engineers , 2002 .

[3] Radionuclide transport in fractured porous media—Analytical solutions for a system of parallel fractures with a constant inlet flux , 1997 .

[4] R. Wyatt. Direct computation of quantal rate constants: Recursive development of the flux autocorrelation function , 1985 .

[5] T. Park,et al. Unitary quantum time evolution by iterative Lanczos reduction , 1986 .

[6] Huazhou Wei. Ghost levels and near-variational forms of the discrete variable representation: Application to H2O , 1997 .

[7] N. Mohankumar,et al. On the use of higher-order formula for numerical derivatives inscientific computing , 2004, Comput. Phys. Commun..

[8] William H. Miller,et al. Quantum mechanical rate constants for bimolecular reactions , 1983 .

[9] C. Pozrikidis. Numerical computation in science and engineering , 1998 .

[10] D. Colbert,et al. A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method , 1992 .