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\begin{document}

\title{Numerical Calculations of the MEW Equation from a New Perspective}



\author[1]{Melike Karta}%
\author[2]{Selcuk KUTLUAY}%
\affil[1]{Agri Ibrahim Cecen Universitesi Matematik Bolumu}%
\affil[2]{Seiyun University Department of Mathematics}%


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  \date{May 18, 2024}


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\begin{abstract}
Numerical computations for natural systems and acquiring travelling wave
solutions of nonlinear wave equations in relation to sciences such as
optics, fluid mechanics, solid state physics, plasma physics, kinetics,
and geology have become very important in the field of mathematical
modeling recently. For this, many methods have been suggested. The
strategy applied for this article is to obtain more perfect numerical
solutions of Modified Equal Width equation (MEW), which is one of the
equations used to model the nonlinear phenomena mentioned. For this
purpose, the Lie-Trotter splitting technique is applied to the MEW
equation. Firstly, the problem is split into two sub-problems, one
linear and the other nonlinear, containing derivative with respect to
time. Secondly, each subproblem is reduced to the algebraic equation
system by using collocation finite element method (FEM) based on the
quintic B-spline approximate functions for spatial discretization and
the convenient classical finite difference approaches for temporal
discretization. Then, the obtained systems are solved with the Lie
Trotter splitting algorithm. Explanatory test problems are considered,
showing that the newly proposed algorithm has superior accuracy than
previous methods, and the numerical results produced by the proposed
algorithm are shown in tables and graphs. In addition, the stability
analysis of the new approach is examined. Therefore, it is appropriate
to state that this new technique can be easily applied to partial
differential equations used in other disciplines in terms of the results
obtained and the cost of Matlab calculation software.%
\end{abstract}%



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