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Numerical solution of the sine-Gordon equation
Affiliation:1. Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan;2. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762, USA;3. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;4. Deanship of Research and Graduate Studies, Applied Science University, PO Box 5055, Bahrain;5. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, People’s Republic of China;6. Science Program, Texas A&M University at Qatar, Doha PO Box 23874, Qatar
Abstract:Two new difference schemes are proposed for the sine-Gordon equation. They have the advantage that there is a discrete energy which is conserved. Their stability and convergence is proved. Also we show some numerical computations using one of these schemes.
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