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

Date

2012-08-01

Author

Pekmen, B.
Tezer, Münevver

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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

Collections

Department of Mathematics, Article