Numerical investigation of nonlinear generalized regularized long wave equation via delta-shaped basis functions

Ömer Oruç

doi:10.11121/ijocta.01.2020.00881

Authors

Ömer Oruç Eğil Vocational and Technical Anatolian High School, Diyarbakır http://orcid.org/0000-0002-6655-3543

DOI:

https://doi.org/10.11121/ijocta.01.2020.00881

Keywords:

Delta-Shaped basis functions, Nonlinear PDE, GRLW equation, Meshless method, Numerical solution

Abstract

In this study we will investigate generalized regularized long wave (GRLW)
equation numerically. The GRLW equation is a highly nonlinear partial
differential equation. We use finite difference approach for time
derivatives and linearize the nonlinear equation. Then for space discretization
we use delta-shaped basis functions which are relatively few studied
basis functions. By doing so we obtain a linear system of equations
whose solution is used for constructing numerical solution of the
GRLW equation. To see efficiency of the proposed method four classic
test problems namely the motion of a single solitary wave, interaction
of two solitary waves, interaction of three solitary waves and Maxwellian
initial condition are solved. Further, invariants are calculated.
The results of numerical simulations are compared with exact solutions
if available and with finite difference, finite element and some collocation
methods. The comparison indicates that the proposed method is favorable
and gives accurate results.

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