An Error Attenuating Predictor-Corrector Approach for Stiff Systems of Ordinary Differential Equations

Abstract

This work involves the use of an error attenuating predictor-corrector approach (EAPCA) for both fixed and variable step-size to solve systems of ordinary differential equations (ODEs) in both linear and nonlinear cases, focusing interest on stiff problems. Apart from the traditional predictor-corrector (TPC) method where each corrector corrects the prediction once at each step, our proposed scheme will refine the results more precisely by infusing a tolerance meeting point on each corrector method which will make corrections until it satisfies the given tolerance. Four well-known stiff systems of initial value problems are chosen as illustrative examples to show the effectiveness of the present method. We compare our results with the results obtained by TPC. This comparison reveals that the EAPCA is much compatible. The EAPCA is a promising method for various systems of linear and nonlinear equations.

Cite as

Mostak Ahmed, Md. Mehadi Hasan, & Md. Abdullah Bin Masud. (2022). An Error Attenuating Predictor-Corrector Approach for Stiff Systems of Ordinary Differential Equations. Journal of Applied Mathematics and Statistical Analysis, 3(2), 1–10. https://doi.org/10.5281/zenodo.6844855