A Numerical Method for the Generalized Regularized Long Wave Equation Using a Reproducing Kernel Function

2008 ◽  
Vol 30 (5) ◽  
pp. 2263-2285 ◽  
Author(s):  
Shusen Xie ◽  
Seokchan Kim ◽  
Gyungsoo Woo ◽  
Sucheol Yi
Keyword(s):  
Wave Equation ◽  
Numerical Method ◽  
Kernel Function ◽  
Reproducing Kernel ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Reproducing Kernel Function

scholarly journals A Good Numerical Method for the Solution of Generalized Regularized Long Wave Equation

2017 ◽  
Vol 11 (6) ◽  
pp. 72 ◽  
Author(s):  
Fuchang Zheng ◽  
Shuhong Bao ◽  
Yulan Wang ◽  
Shuguang Li ◽  
Zhiyuan Li
Keyword(s):  
Wave Equation ◽  
Numerical Method ◽  
High Precision ◽  
Science And Technology ◽  
Convergence Speed ◽  
Fast Convergence ◽  
Numerical Examples ◽  
Long Wave ◽  
Regularized Long Wave Equation

The generalized regularized long wave equation is very important that can be applied in the field of physics,science and technology. Some authors have put forward many different numerical method, but the precision isnot enough high. In this paper, we will illustrate the high-precision numerical method to solve the generalizedregularized long wave equation. Three numerical examples are studied to demonstrate the accuracy of thepresent method. Results obtained by our method indicate new algorithm has the following advantages: smallcomputational work, fast convergence speed and high precision.

Ritz Legendre Multiwavelet Method for the Damped Generalized Regularized Long-Wave Equation

2011 ◽  
Vol 7 (1) ◽  
Author(s):  
S. A. Yousefi ◽  
Z. Barikbin
Keyword(s):  
Wave Equation ◽  
Galerkin Method ◽  
Numerical Method ◽  
Variable Coefficient ◽  
Algebraic Equations ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
The Galerkin Method

In this paper, a numerical method is proposed to approximate the solution of the nonlinear damped generalized regularized long-wave (DGRLW) equation with a variable coefficient. The method is based upon Ritz Legendre multiwavelet approximations. The properties of Legendre multiwavelet are first presented. These properties together with the Galerkin method are then utilized to reduce the nonlinear DGRLW equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Euler operators and conservation laws of the BBM equation

1979 ◽  
Vol 85 (1) ◽  
pp. 143-160 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Calculus Of Variations ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Formal Calculus ◽  
Euler Operators ◽  
Bbm Equation

AbstractThe BBM or Regularized Long Wave Equation is shown to possess only three non-trivial independent conservation laws. In order to prove this result, a new theory of Euler-type operators in the formal calculus of variations will be developed in detail.

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