Numerical study of sine-Gordon equations using Bessel collocation method

The nonlinear space time dynamics have been discussed in terms of a hyper-bolic equation known as a sine-Gordon equation. The proposed equation has been discretized using the Bessel collocation method with Bessel poly-nomials as base functions. The proposed hyperbolic equation has been transformed into a system of parabolic equations using a continuously dif-ferentiable function. The system of equations involves one linear and the other nonlinear diffusion equation. The convergence of the present tech-nique has been discussed through absolute error, L2-norm, and L∞-norm.The numerical values obtained from the Bessel collocation method have been compared with the values already given in the literature. The present technique has been applied to different problems to check its applicability. Numerical values obtained from the Bessel collocation method have been presented in tabular as well as in graphical form.