Numerical simulation of two dimensional sine-Gordon solitons using modified cubic B-spline differential quadrature method

In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM) is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differenti...

Full description

Saved in:
Bibliographic Details
Published in:AIP advances 2015-01, Vol.5 (1), p.017121-017121-14
Main Authors: Shukla, H. S., Tamsir, Mohammad, Srivastava, Vineet K.
Format: Article
Language:English
Subjects:
Basis functions
Boundary conditions
Computer simulation
Differential equations
Mathematical models
Ordinary differential equations
Runge-Kutta method
Simulation
Solitary waves
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM) is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differential quadrature method to compute the weighting coefficients. Accordingly, two dimensional sine-Gordon equation is transformed into a system of second order ordinary differential equations (ODEs). The resultant system of ODEs is solved by employing an optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme (SSP-RK54). Numerical simulation is discussed for both damped and undamped cases. Computational results are found to be in good agreement with the exact solution and other numerical results available in the literature.
ISSN:2158-3226
2158-3226
DOI:10.1063/1.4906256