An efficient approach for solving nonlinear multidimensional Schrödinger equations. (1st November 2021) - Karabaş, Neslişah İmamoğlu; Korkut, Sıla Övgü; Tanoğlu, Gamze; Aziz, Imran; Siraj-ul-Islam,
Abstract: An efficient numerical method is proposed for the solution of the nonlinear cubic Schrödinger equation. The proposed method is based on the Fréchet derivative and the meshless method with radial basis functions. An important characteristic of the method is that it can be extended from one-dimensional problems to multi-dimensional ones easily. By using the Fréchet derivative and Newton–Raphson technique, the nonlinear equation is converted into a set of linear algebraic equations which are solved iteratively. Numerical examples reveal that the proposed method is efficient and reliable with respect to the accuracy and stability.