High order closed Newton–Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation Export

@article{citeulike:4109210, abstract = {In this paper, we investigate the connection between • closed Newton–Cotes formulae, The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant literature and the references here). In this paper we study the closed Newton–Cotes formulae and we write them as symplectic multilayer structures. Based on the closed Newton–Cotes formulae, we also develop trigonometrically-fitted symplectic methods. An error analysis for the one-dimensional Schr\"{o}dinger equation of the new developed methods and a comparison with previous developed methods is also given. We apply the new symplectic schemes to the well-known radial Schr\"{o}dinger equation in order to investigate the efficiency of the proposed method to these type of problems.}, author = {Simos, T. E.}, citeulike-article-id = {4109210}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.amc.2008.06.020}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0096300308004815}, day = {01}, doi = {10.1016/j.amc.2008.06.020}, issn = {00963003}, journal = {Applied Mathematics and Computation}, keywords = {numerical\_schrodinger}, month = {March}, number = {1}, pages = {137--151}, posted-at = {2009-02-27 06:25:00}, priority = {2}, title = {High order closed Newton–Cotes trigonometrically-fitted formulae for the numerical solution of the Schr\"{o}dinger equation}, url = {http://dx.doi.org/10.1016/j.amc.2008.06.020}, volume = {209}, year = {2009} }

TY - JOUR ID - citeulike:4109210 L3 - citeulike-article-id:4109210 N2 - In this paper, we investigate the connection between • closed Newton–Cotes formulae, The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant literature and the references here). In this paper we study the closed Newton–Cotes formulae and we write them as symplectic multilayer structures. Based on the closed Newton–Cotes formulae, we also develop trigonometrically-fitted symplectic methods. An error analysis for the one-dimensional Schrödinger equation of the new developed methods and a comparison with previous developed methods is also given. We apply the new symplectic schemes to the well-known radial Schrödinger equation in order to investigate the efficiency of the proposed method to these type of problems. IS - 1 JF - Applied Mathematics and Computation SN - 00963003 EP - 151 TI - High order closed Newton–Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation VL - 209 SP - 137 KW - numerical_schrodinger AU - Simos, TE PY - 2009/03/01/ UR - http://dx.doi.org/10.1016/j.amc.2008.06.020 ER -