Solving ordinary differential equations by ZED 4IgSFD_L method

Ordinary differential equations (ODEs) are commonly used in physical system and automation researches, describing the relationship among variables. Hence there are practical significances to discuss and to research the solutions of ODEs. The initial value problem (IVP) is one of the important parts, and we usually use traditional methods, e.g. Euler method, to obtain the solutions. In this paper, we propose a new method named ZFD (Zhang finite difference) 4IgSFD_L method. Note that this method is developed by using ZFD formula 4IgSFD_L (4-instant g-square finite difference with subtype L) based on Taylor expansion, with g denoting sampling gap and g <; 1. It can be used to solve IVP with higher accuracy substantiated by numerical experiments. While Euler method can be used to solve IVP with an error of order O(g), ZFD 4IgSFD_L method can be applied to solving IVP with an error of order O(g
²
).