Solving SEI Model using Non-Standard Finite Difference and High Order Extrapolation with Variable Step Length

Abstract

A high-level method was obtained to solve the SEI model problem involving Symmetrization measures in numerical calculations through the Implicit Midpoint Rule method (IMR). It is obtained using Non-Standard Finite Difference Schemes (NSFD) with Extrapolation techniques combined. In solving differential equation problems numerically, the Extrapolated SEI model method is able to generate more accurate results than the existing numerical method of SEI model. This study aims to investigate the accuracy and efficiency of computing between Extrapolated One-Step Active Symmetry Implicit Midpoint Rule method (1ASIMR), Extrapolated One-Step Active Symmetry Implicit Midpoint Rule method (2ASIMR), Extrapolated One-Step Passive Symmetry Midpoint Rule method (1PSIMR) and the extrapolated Two-Step Passive Symmetry Midpoint Rule method (2PSIMR). The results show that the 1ASIMR method is the most accurate method. For the determination of the efficiency of 2ASIMR and 2PSIMR methods have high efficiency. At the end of the study, the results from the numerical method obtained show that Extrapolation using Non-Standard Finite Difference has higher accuracy than the existing Implicit Midpoint Rule method.