Qualitative analysis of a novel numerical method for solving non-linear ordinary differential equations

Abstract

The dynamics of innumerable real-world phenomena is represented with the help of non-linear ordinary differential equations (NODEs). There is a growing trend of solving these equations using accurate and easy to implement methods. The goal of this research work is to create a numerical method to solve the first-order NODEs (FNODEs) by coupling of the well-known trapezoidal method with a newly developed semi-analytical technique called the Laplace optimized decomposition method (LODM). The novelty of this coupling lies in the improvement of order of accuracy of the scheme when the terms in the series solution are increased. The article discusses the qualitative behavior of the new method, i.e., consistency, stability and convergence. Several numerical test cases of the non-linear differential equations are considered to validate our findings.