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

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.