Numerical study of sine-Gordon equations using Bessel collocation method

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Arora S.; Bala I.

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2023 | Volume:13 | Issue:4 Page(s): 728-746

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Information Journal Paper

Title

Numerical study of sine-Gordon equations using Bessel collocation method

Author(s)

Arora S. | Bala I. | Issue Writer Certificate

Keywords

sine-Gordon equation

Bessel polynomials

Wave equation

Or-thogonal Collocation

Abstract

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.

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