Numerical treatment of Hunter Saxton equation using cubic trigonometric B-spline collocation method
Source abstract
Abstract
In this article, authors proposed a computational model based on cubic trigonometric B-spline collocation method to solve Hunter Saxton equation. The nonlinear second order partial differential equation arises in modeling of nematic liquid crystals and describes some aspects of orientation wave. The problem is decomposed into system of linear equations using cubic trigonometric B-spline collocation method with quasilinearization. To show the efficiency of the proposed method, two numerical examples have been tested for different values of t. The results are described using error tables and graphs and compared with the results existed in literature. It is evident that results are in good agreement with analytical solution and better than Arbabi, Nazari, and Davishi, Optik 127, 5255–5258 (2016). In current problem, it is also observed that the cubic trigonometric B-spline gives better results as compared to cubic B-spline.
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Research context
OpenAlex topics: Nonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Fractional Differential Equations Solutions
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Affiliations
Department of Mathematics, COMSATS Institute of Information Technology 1 , Sahiwal 57000, Pakistan
Department of Mathematics, The Government Sadiq College Women University 2 , Bahawalpur 63100, Pakistan
Department of Mathematics, University of Sargodha, Lylpur Campus 3 , 38000, Pakistan
Department of Mathematics, University of Lahore, Pakpattan Campus 4 , 57400, Pakistan
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