Effect of Numerical Truncation Error on Implicit Finite Difference Methods in Groundwater Transport Models

A correction for truncation errors associated with implicit finite difference method (FDM) of the groundwater transport equation with reaction term, which is generally used in groundwater transport models, is developed here from a Taylor series analysis. An application example is formulated to illustrate the effect of truncation errors on the numerical solution of implicit FDM. The study compares the effect of truncation error on numerical model accuracy of implicit FDM and explicit FDM for groundwater transport equation with reaction term. The explicit FDM constitutes large deviation from analytical solution without truncation error correction. The relative error analysis reveals that error reduces from 75% to 30% after truncation error correction. Therefore, we can conclude that numerical truncation error correction has significant impact on accuracy of groundwater transport models based on explicit FDM than those based on implicit FDM.