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

#### 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.

#### Keywords

#### Full Text:

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DOI: http://dx.doi.org/10.11121/ijocta.01.2020.00881

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