quantum solutions of a nonlinear schrödinger equation

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.