Quantum solutions of a nonlinear Schrödinger equation

Iranian Journal of Numerical Analysis and Optimization

مقاله 1، دوره 14، Issue 2 - شماره پیاپی 29، شهریور 2024، صفحه 330-346   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.84855.1324

نویسندگان

S. Arfaoui^{1، 2}؛ Ben Mabrouk^{* 3، 4، 5}

¹Laboratory of Algebra, Number Theory and Nonlinear Analysis, Department of Math-ematics, Faculty of Sciences, University of Monastir, Avenue of the Environment, 5019 Monastir, Tunisia.

²nstitut Supérieur d’Informatique du Kef, Université de Jendouba, 5 Rue Saleh Ayech - 7100 Kef, Tunisia

³Laboratory of Algebra, Number Theory and Nonlinear Analysis, Department of Math- ematics, Faculty of Sciences, University of Monastir, Avenue of the Environment, 5019 Monastir, Tunisia.

⁴Department of Mathematics, Higher Institute of Applied Mathematics and Computer Science, University of Kairouan, Street Assad Ibn Alfourat, Kairouan 3100, Tunisia.

⁵Department of Mathematics, Faculty of Sciences, University of Tabuk, King Faisal Road, Tabuk 47512, Saudi Arabia.

چکیده

In the present paper, we precisely conduct a quantum calculus method for the numerical solutions of PDEs. A nonlinear Schrödinger equation is considered. Instead of the known classical discretization methods based on the finite difference scheme, Adomian method, and third modified ver-sions, we consider a discretization scheme leading to subdomains according to q-calculus and provide an approximate solution due to a specific value of the parameter q. Error estimates show that q-calculus may produce effi-cient numerical solutions for PDEs. The q-discretization leads effectively to higher orders of convergence provided with faster algorithms. The numer-ical tests are applied to both propagation and interaction of soliton-type solutions.

کلیدواژه‌ها

NLS equation؛ Quantum calculus؛ Numerical solution؛ Error estimates

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