arXiv subjects
Publications and source records attributed to P. Cerejeiras.
The aim of this work is to study the numerical solution of the nonlinear Schrodinger problem using a combination between Witt basis and finite difference approximations. We construct a discrete fundamental solution for the non-stationary Schrodinger operator and we show the convergence of the numerical scheme. Numerical examples are given at the end of the paper.
In this paper we will study the existence of fundamental solutions for the explicit and implicit backward time dependent Schodinger equation, via discrete Fourier transform and its symbol for the Laplace operator. In both cases we will prove that the discrete fundamental solutions obtained converges to the continuous fundamental solution in the $l_1-$norm sense.
In this paper we give a generalization of the classical Borel-Carathéodory Theorem in complex analysis to higher dimensions in the framework of Quaternionic Analysis.
We consider a factorization of the non-stationary Schrodinger operator based on the parabolic Dirac operator introduced by Cerejeiras/ Kahler/ Sommen. Based on the fundamental solution for the parabolic Dirac operators, we shall construct appropriated Teodorescu and Cauchy-Bitsadze operators. Afterwards we will describe how to solve the nonlinear Schrodinger equation using Banach fixed point theorem.