Abstract
In this work, we use a reproducing kernel method for investigating the sine-Gordon equation with initial and boundary conditions. Numerical experiments are studied to show the efficiency of the technique. The acquired results are compared with the exact solutions and results obtained by different methods. These results indicate that the reproducing kernel method is very effective.
Highlights
The nonlinear one-dimensional sine-Gordon (SG) equation came into sight in the differential geometry and attracted a lot of attention because of the collisional behaviors of solitons that arise from this equation
Numerical solutions of the SG equation have been widely investigated in recent years [ – ]
6 Conclusion Linear and nonlinear SG equations were investigated by reproducing kernel method (RKM) in this work
Summary
The nonlinear one-dimensional sine-Gordon (SG) equation came into sight in the differential geometry and attracted a lot of attention because of the collisional behaviors of solitons that arise from this equation. The authors of [ ] introduced a numerical method for solving the SG equation by using collocation and radial basis functions. A numerical technique using radial basis functions for the solution of the two-dimensional SG equation has been shown in [ ]. By using the reproducing kernel method (RKM). Reproducing kernel functions are very important for numerical results.
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