Quantum solutions of a nonlinear Schrödinger equation
نویسندگان
1 Laboratory of Algebra, Number Theory and Nonlinear Analysis, Department of Math-ematics, Faculty of Sciences, University of Monastir, Avenue of the Environment, 5019 Monastir, Tunisia.
2 nstitut Supérieur d’Informatique du Kef, Université de Jendouba, 5 Rue Saleh Ayech - 7100 Kef, Tunisia
doi
10.22067/ijnao.2023.84855.1324چکیده
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.
