THE PREDICTOR-CORRECTOR BACKWARD DIFFERENCE FORMULAS TO ESTIMATE THE TREND OF RIVER WATER QUALITY

The time-series trend analysis is a mathematical technique that attempts to estimate future data movement based on observed previous and current data. This can include analysing long-terms changes in river water quality in order to emphasise river management in the future. Therefore, in this study, the backward difference formula (BDF) with forward and central difference approximations is derived to estimate a of 20-year trend in water quality index (WQI) data at the Selangor River basin in Malaysia. As an adaptation of the conventional BDF and predictor-corrector scheme, the Euler’s method with a central difference formula is introduced as a predictor formula to forecast future values. Subsequently, BDF with central and forward difference formulas are specifically designed as corrector formulas to adjust the predicted future values. The performance of the method is evaluated with absolute error and average error accuracy measure indicators. The numerical results validated the proposed method and proved its reliability in estimating the time series trend analysis owing to its reasonable accuracy. In conclusion, the outcomes of this study can provide the authorities with a technical reference for monitoring, maintaining and improving the river water quality in Selangor and other states.