Hybrid-Block Method for the Solution of Second Order Non-linear Differential Equations
A.A. James James
Department of Mathematics, American University of Nigeria, Yola, Adamawa State, Nigeria.
G. Ajileye *
Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.
A. M. Ayinde
Department of Mathematics, Moddibo-Adama University, Yola, Nigeria.
W. Dunama
Department of Mathematics, Moddibo-Adama University, Yola, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The Duffing equation is one of the most unique and special non-linear differential equations in light of its many real-world applications in areas ranging from physics to economics. This paper sets out to investigate and study some existing numerical methods proposed by different authors over the years and subsequently develop an alternative computational method that can be used to solve duffing oscillator equations. This new method was developed by adopting the power series as the basis function and integrating it within quarter-step intervals using the interpolation and collocation approach. The analysis of the new method was carried out and found to be zero-stable, consistent, and convergent. Four duffing problems were used to test the efficiency of the new method, and the results were found to be computationally reliable.
Keywords: Duffing equations, collocation, block method, interpolation, approximate solution