A new three-point sixth-order THAGE iteration method for mildly nonlinear two-point boundary value problems with engineering applications

We study a new sixth-order compact discretization using uniform three-grid point for the mildly nonlinear differential equation ϕ′′=g(t,ϕ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ''=g(t,\phi )$$\end{document}, subject to the values of ϕ given at two end points of the regular solution interval. We also discuss three-step AGE (THAGE) iteration method as an application to the resulting difference equation as a powerful numerical computation device. In this algorithm, the common term is evaluated first to save the CPU time in comparison with the corresponding two-step algorithm. In addition, the error analysis is studied. Numerical performance is compared with the exact solution, and with the two-step AGE and SOR iteration methods.