scholarly journals A finite difference solution of the regularized long-wave equation

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
S. Kutluay ◽  
A. Esen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Undular Bore ◽  
One Dimensional ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Finite Difference Solution ◽  
Implicit Finite Difference ◽  
Waves Interaction ◽  
The One

A linearized implicit finite difference method to obtain numerical solution of the one-dimensional regularized long-wave (RLW) equation is presented. The performance and the accuracy of the method are illustrated by solving three test examples of the problem: a single solitary wave, two positive solitary waves interaction, and an undular bore. The obtained results are presented and compared with earlier work.

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

2020 ◽  
Vol 10 (2) ◽  
pp. 244-258 ◽  
Author(s):  
Ömer Oruç
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Finite Difference ◽  
Solitary Waves ◽  
Basis Functions ◽  
Long Wave ◽  
Highly Nonlinear ◽  
Regularized Long Wave Equation ◽  
Waves Interaction ◽  
Grlw Equation

In this study we will investigate generalized regularized long wave (GRLW)equation numerically. The GRLW equation is a highly nonlinear partialdifferential equation. We use finite difference approach for timederivatives and linearize the nonlinear equation. Then for space discretizationwe use delta-shaped basis functions which are relatively few studiedbasis functions. By doing so we obtain a linear system of equationswhose solution is used for constructing numerical solution of theGRLW equation. To see efficiency of the proposed method four classictest problems namely the motion of a single solitary wave, interactionof two solitary waves, interaction of three solitary waves and Maxwellianinitial condition are solved. Further, invariants are calculated.The results of numerical simulations are compared with exact solutionsif available and with finite difference, finite element and some collocationmethods. The comparison indicates that the proposed method is favorableand gives accurate results.

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