Theoretical Error Analysis of Hybrid Finite Difference–Asymptotic Interpolation Method for Non-Newtonian Fluid Flow

Abstract

In this paper, we utilized a hybrid method for the unsteady flow of the non-Newtonian third-grade fluid that combines the finite difference with the asymptotic interpolation method. This hybrid method is used to satisfy the semiunbound domain condition of the fluid flow’s length approaching infinity. The primary issue with this research is how much of the hybrid approach’s error may be accepted to guarantee that the method is significant. This paper discussed theoretical error analysis for numerical solutions, including the range and norm of error. The perturbation method’s concept is used to assess the hybrid method’s error. It is discovered that the hybrid approach’s relative error norm is lower than that of the finite difference method. In terms of the error standard, the hybrid approach is more consistent. Error analysis is performed to check for the accuracy as well as the platform for variable mesh size finite difference method in the future research.