Numerical Study of sine-Gordon Equations using Bessel Collocation Method

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 خرداد 1402

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.81484.1229

نویسندگان

Shelly Arora؛ Indu Bala^*

Department of Mathematics, Punjabi University, Patiala, Punjab-147002, INDIA.

چکیده

The non-linear space-time dynamics have been discussed in terms of a hyperbolic equation known as the sine Gordon equation. The proposed equation has been discretized using the Bessel collocation method with Bessel polynomials as base functions. The proposed hyperbolic equation has been transformed into a system of parabolic equations using a continuously differentiable function. The system of equations involves one linear and the other non-linear diffusion equation. The convergence of the present technique has been discussed through absolute error, $L_2$-norm, and $L_{\infty}$-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.

کلیدواژه‌ها

sine– Gordon equation؛ Bessel polynomials؛ Wave equation؛ Orthogonal Collocation