A new numerical approach to the solution of the nonlinear Kawahara equation by using combined Taylor–Dickson approximation

Iranian Journal of Numerical Analysis and Optimization

مقاله 2، دوره 14، Issue 1 - شماره پیاپی 28، خرداد 2024، صفحه 20-43   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.83184.1287

نویسندگان

D. Priyadarsini؛ M. Routaray؛ P.K. Sahu^*

Department of Mathematics, School of Applied Sciences, KIIT University, Odisha-751024, India.

چکیده

This article presents a novel numerical approach to the solution of the nonlinear Kawahara equation. The desired approximations are obtained from the combination of Dickson polynomials and Taylor’s expansion. The combined approach is based on Taylor’s expansion for discretizing the time derivative and Dickson polynomials for space derivatives. The problem will be converted into a system of linear algebraic equations for each time step via some suitable collocation points. Error estimation is presented after obtaining the approximate solution. The newly proposed technique is compared with some existing numerical methods to show the method’s applicability, accuracy, and efficacy. Two problems are solved to demon-strate the method’s power and effect, and the results are presented as a table and graphics.

کلیدواژه‌ها

Taylor’s expansion؛ Dickson polynomials؛ Kawahara equation؛ Discretization

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