A fast converging method for generating solutions to the Riccati equation

H. Eleuch; H. Bahlouli; Y. V. Rostovtsev

doi:10.1016/j.amc.2013.08.004

A fast converging method for generating solutions to the Riccati equation

H. Eleuch^*
, H. Bahlouli
, Y. V. Rostovtsev

^*Corresponding author for this work

Department of Physics

Research output: Contribution to journal › Article › peer-review

Abstract

We devise an approximate and fast converging iterative approach to solve the Riccati equation. This solution provides a systematic way to generate isospectral potentials in quantum mechanics. The proposed solutions derived by our approach are compared with exact solutions for various potentials.

Original language	English
Pages (from-to)	548-552
Number of pages	5
Journal	Applied Mathematics and Computation
Volume	222
DOIs	https://doi.org/10.1016/j.amc.2013.08.004
State	Published - 2013

Bibliographical note

Funding Information:
The generous support provided by the Saudi Center for Theoretical Physics (SCTP) is highly appreciated by HE and HB. HB acknowledges partial support by King Fahd University of Petroleum & Minerals under project RG1108–1 and RG1108–2. YR gratefully acknowledges the support from the UNT Research Initiation Grant and the summer fellowship UNT program.

Keywords

Nonlinear equations
Riccati equation
Schrödinger equation
Supersymmetric quantum mechanics

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2013.08.004

Cite this

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title = "A fast converging method for generating solutions to the Riccati equation",

abstract = "We devise an approximate and fast converging iterative approach to solve the Riccati equation. This solution provides a systematic way to generate isospectral potentials in quantum mechanics. The proposed solutions derived by our approach are compared with exact solutions for various potentials.",

keywords = "Nonlinear equations, Riccati equation, Schr{\"o}dinger equation, Supersymmetric quantum mechanics",

author = "H. Eleuch and H. Bahlouli and Rostovtsev, \{Y. V.\}",

note = "Funding Information: The generous support provided by the Saudi Center for Theoretical Physics (SCTP) is highly appreciated by HE and HB. HB acknowledges partial support by King Fahd University of Petroleum \& Minerals under project RG1108–1 and RG1108–2. YR gratefully acknowledges the support from the UNT Research Initiation Grant and the summer fellowship UNT program.",

year = "2013",

doi = "10.1016/j.amc.2013.08.004",

language = "English",

volume = "222",

pages = "548--552",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

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T1 - A fast converging method for generating solutions to the Riccati equation

AU - Eleuch, H.

AU - Bahlouli, H.

AU - Rostovtsev, Y. V.

N1 - Funding Information: The generous support provided by the Saudi Center for Theoretical Physics (SCTP) is highly appreciated by HE and HB. HB acknowledges partial support by King Fahd University of Petroleum & Minerals under project RG1108–1 and RG1108–2. YR gratefully acknowledges the support from the UNT Research Initiation Grant and the summer fellowship UNT program.

PY - 2013

Y1 - 2013

N2 - We devise an approximate and fast converging iterative approach to solve the Riccati equation. This solution provides a systematic way to generate isospectral potentials in quantum mechanics. The proposed solutions derived by our approach are compared with exact solutions for various potentials.

AB - We devise an approximate and fast converging iterative approach to solve the Riccati equation. This solution provides a systematic way to generate isospectral potentials in quantum mechanics. The proposed solutions derived by our approach are compared with exact solutions for various potentials.

KW - Nonlinear equations

KW - Riccati equation

KW - Schrödinger equation

KW - Supersymmetric quantum mechanics

UR - https://www.scopus.com/pages/publications/84883195548

U2 - 10.1016/j.amc.2013.08.004

DO - 10.1016/j.amc.2013.08.004

M3 - Article

AN - SCOPUS:84883195548

SN - 0096-3003

VL - 222

SP - 548

EP - 552

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

A fast converging method for generating solutions to the Riccati equation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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