Solving ordinary differential equations by ZFD formula 4NgSFD

In this paper, a new Zhang finite difference (ZFD) formula with higher accuracy, termed 4-node g-square finite difference (4NgSFD), is presented and applied to solving ordinary differential equations (ODEs). Such a method is thus considered as ZFD 4NgSFD method. For comparison, the conventional Euler method is also presented. In addition, numerical experiments are carried out, of which the results substantiate that the accuracy of ZFD 4NgSFD method is indeed higher than that of Euler method for solving ODEs. Note that the presented ZFD 4NgSFD method can be applied in ODE numerical solver software.