Mean-Based Efficient Hybrid Numerical Method For Solving First-Order Ordinary Differential Equations

Abstract

The center of interest of this work is to introduce a mean-based efficient hybrid numerical method for solving first-order ordinary differential equations with initial conditions. This method is generated by the mean of the modified slope of modified Euler’s method and the mean of main incremental functions of RK-2 method and a second-order contra harmonic mean method. The factors related to the numerical method have been analyzed to observe its performance and found that the method satisfies all its factors. It also performs with better accuracy than modified Euler’s methods, a second stage second-order contra harmonic mean method, and RK-2 method. The proposed method performed with better accuracy than the existing methods, but it is also better workable on some other second-order well-known methods.