Differential quadrature solution of nonlinear Klein-Gordon and sine-Gordon equations

Date

2012-08-01

Author

Pekmen, B.
Tezer, Münevver

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

164
views

0
downloads

Differential quadrature method (DQM) is proposed to solve the one-dimensional quadratic and cubic Klein-Gordon equations, and two-dimensional sine-Gordon equation. We apply DQM in space direction and also blockwise in time direction. Initial and derivative boundary conditions are also approximated by DQM. DQM provides one to obtain numerical results with very good accuracy using considerably small number of grid points. Numerical solutions are obtained by using Gauss-Chebyshev-Lobatto (GCL) grid points in space intervals, and GCL grid points in each equally divided time blocks.

Subject Keywords

Klein-Gordon equation, Sine-Gordon equation, Differential quadrature method

URI

https://hdl.handle.net/11511/41479

Journal

COMPUTER PHYSICS COMMUNICATIONS

DOI

https://doi.org/10.1016/j.cpc.2012.03.010

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Differential - Operator solutions for complex partial differential equations Celebi, O; Sengul, S (1998-07-10) The solutions of complex partial differential equations of order four are obtained by using polynomial differential operators. A correspondence principle is also derived for the solutions of two different differential equations, imposing conditions on the coefficients.
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems Bozkaya, Canan (2005-03-18) The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential IKHDAİR, SAMEER; Sever, Ramazan (2008-03-01) The Klein-Gordon equation in D-dimensions for a recently proposed ring-shaped Kratzer potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the non-central equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three dimensions given by other works.
Differential equations with discontinuities and population dynamics Aruğaslan Çinçin, Duygu; Akhmet, Marat; Department of Mathematics (2009) In this thesis, both theoretical and application oriented results are obtained for differential equations with discontinuities of different types: impulsive differential equations, differential equations with piecewise constant argument of generalized type and differential equations with discontinuous right-hand sides. Several qualitative problems such as stability, Hopf bifurcation, center manifold reduction, permanence and persistence are addressed for these equations and also for Lotka-Volterra predator-...
Differential Quadrature Solution of Hyperbolic Telegraph Equation Pekmen, B.; Tezer, Münevver (2012-01-01) Differential quadrature method (DQM) is proposed for the numerical solution of one- and two-space dimensional hyperbolic telegraph equation subject to appropriate initial and boundary conditions. Both polynomial-based differential quadrature (PDQ) and Fourier-based differential quadrature (FDQ) are used in space directions while PDQ is made use of in time direction. Numerical solution is obtained by using Gauss-Chebyshev-Lobatto grid points in space intervals and equally spaced and/or GCL grid points for th...

Citation Formats

B. Pekmen and M. Tezer, “Differential quadrature solution of nonlinear Klein-Gordon and sine-Gordon equations,” COMPUTER PHYSICS COMMUNICATIONS, pp. 1702–1713, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41479.