Quantum solutions of a nonlinear Schrodinger equation
Sabrine Arfaoui
TL;DR
This paper introduces a q-calculus based numerical method for solving nonlinear Schrödinger equations, offering an alternative to classical discretization techniques with promising efficiency and accuracy.
Contribution
It develops a novel q-calculus approach for PDEs, providing error estimates and demonstrating its potential as an effective numerical solution method.
Findings
q-calculus yields efficient numerical solutions
Error estimates support method accuracy
Potential for improved PDE discretization
Abstract
In the present paper, we precisely conduct a q-calculus method for the numerical solutions of PDEs. A nonlinear Schrodinger equation is considered. Instead of the classical discretization methods we consider 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 efficient numerical solutions for PDEs.
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Taxonomy
TopicsNumerical Methods and Algorithms · Mathematical and Theoretical Analysis · Polynomial and algebraic computation