scholarly journals The Spectral Method for Solving Sine-Gordon Equation Using a New Orthogonal Polynomial

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Zoleikha Soori ◽  
Azim Aminataei
Keyword(s):  
Orthogonal Polynomial ◽  
Spectral Method ◽  
Numerical Scheme ◽  
Gordon Equation ◽  
Weighting Function ◽  
Sine Gordon Equation ◽  
One Dimensional

We have presented a numerical scheme for solving one-dimensional nonlinear sine-Gordon equation. We apply the spectral method with a basis of a new orthogonal polynomial which is orthogonal over the interval with weighting function one. The results show the accuracy and efficiency of the proposed method.

Chebyshev Wavelet Quasilinearization Scheme for Coupled Nonlinear Sine-Gordon Equations

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
K. Harish Kumar ◽  
V. Antony Vijesh
Keyword(s):  
Basis Function ◽  
Numerical Scheme ◽  
Function Method ◽  
Gordon Equation ◽  
Basic Function ◽  
Sine Gordon Equation ◽  
One Dimensional ◽  
Improve Accuracy ◽  
Chebyshev Wavelet ◽  
Grid Points

Radial basis function (RBF) has been found useful for solving coupled sine-Gordon equation with initial and boundary conditions. Though this approach produces moderate accuracy in a larger domain, it requires more grid points. In the present study, we develop an alternative numerical scheme for solving one-dimensional coupled sine-Gordon equation to improve accuracy and to reduce grid points. To achieve these objectives, we make use of a wavelet scheme and solve coupled sine-Gordon equation. Based on the numerical results from the wavelet-based scheme, we conclude that our proposed method is more efficient than the radial basic function method in terms of accuracy.

Sign in / Sign up

Export Citation Format

Share Document