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Chebyshev Split-step Scheme for the Sine-Gordon Equation in 2+1 Dimensions
-
Pablo Suarez
,
Stephen Johnson
Veröffentlicht/Copyright:
21. Februar 2013
Abstract
This article studies the numerical solution of the two-dimensional sine-Gordon equation (SGE) using a split-step Chebyshev Spectral Method. In our method we split the 2D SGE by considering one dimension at a time, first along x and then along y. In each fractional step we solve a 1D SGE. Time integration is handled by a finite difference scheme. The numerical solution is then compared with many of the known numerical solutions found throughout the literature. Our method is simple to implement and second order accurate in time and has spectral convergence. Our method is both fast and accurate.
Received: 2011-8-16
Accepted: 2012-12-19
Published Online: 2013-2-21
Published in Print: 2013-2-22
©2013 by De Gruyter
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Artikel in diesem Heft
- Frontmatter
- Vapor Films under Influence of High Heat Fluxes: Nongravity Surface Waves and Film Explosive Disintegration
- Dynamic Constitutive Behavior and Fracture of Lanthanum Metal Subjected to Impact Compression at Different Temperatures and Impact Tension
- An Application of the Modified Reductive Perturbation Method to a Generalized Boussinesq Equation
- Switching Design for the Asymptotic Stability and Stabilization of Nonlinear Uncertain Stochastic Discrete-time Systems
- A Novel Two-fluid Model for the Identification of Possible Multiple Solutions in Slightly Inclined Pipelines
- Adaptive Synchronization of Filippov Systems with Unknown Parameters via Sliding Mode Control
- Chebyshev Split-step Scheme for the Sine-Gordon Equation in 2+1 Dimensions
- The Numerical Connection between Map and its Differential Equation: Logistic and Other Systems
- Exact Travelling Wave Solutions for the Modified Fornberg-Whitham Equation
Artikel in diesem Heft
- Frontmatter
- Vapor Films under Influence of High Heat Fluxes: Nongravity Surface Waves and Film Explosive Disintegration
- Dynamic Constitutive Behavior and Fracture of Lanthanum Metal Subjected to Impact Compression at Different Temperatures and Impact Tension
- An Application of the Modified Reductive Perturbation Method to a Generalized Boussinesq Equation
- Switching Design for the Asymptotic Stability and Stabilization of Nonlinear Uncertain Stochastic Discrete-time Systems
- A Novel Two-fluid Model for the Identification of Possible Multiple Solutions in Slightly Inclined Pipelines
- Adaptive Synchronization of Filippov Systems with Unknown Parameters via Sliding Mode Control
- Chebyshev Split-step Scheme for the Sine-Gordon Equation in 2+1 Dimensions
- The Numerical Connection between Map and its Differential Equation: Logistic and Other Systems
- Exact Travelling Wave Solutions for the Modified Fornberg-Whitham Equation
