On the Analysis of Numerical Methods for Solving First Order Non-Linear Ordinary Differential Equations
A. Udoh, Ndipmong *
Federal University Otuoke, Bayelsa State, Nigeria.
P. Egbuhuzor, Udechukwu
Federal University Otuoke, Bayelsa State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In determining the numerical solution of a nonlinear first order differential equation, there is need to compare and adopt an efficient method of solution for a particular class of this equation. Hence, the result of a comparative study on the application of four numerical methods, namely the Adomian decomposition method (ADM), the variational iteration method (VIM), the Modified Euler's method (MEM), and the Differential transformation method (DTM) on first order nonlinear differential equations are presented in this work. The results show that the DTM proves to be the most efficient of the four methods applied in this work based on their absolute error values, reliability, sufficiency and simplicity.
Keywords: The Adomian decomposition method, the variation iteration method, the modified euler’s method and the differential transformation method