Construction of exact solutions to eigenvalue problems by the asymptotic iteration method

被引：185

作者：

Ciftci, H

Hall, RL

Saad, N

机构：

[1] Concordia Univ, Dept Math & Stat, Montreal, PQ H3G 1M8, Canada

[2] Univ Prince Edward Isl, Dept Math & Stat, Charlottetown, PE C1A 4P3, Canada

[3] Gazi Univ, Fen Edebiyat Fak Fizik Bolumu, TR-06500 Ankara, Turkey

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2005年 / 38卷 / 05期

关键词：

D O I：

10.1088/0305-4470/38/5/015

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We apply the asymptotic iteration method (AIM) (Ciftci, Hall and Saad 2003 J. Phys. A: Math. Gen. 36 11807) to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue problems which includes Schrodinger problems with Coulomb, harmonic oscillator or Poschl-Teller potentials, as well as the special eigenproblems studied recently by Bender et al (2001 J. Phys. A: Math. Gen. 34 9835) and generalized in the present paper to arbitrary dimension.

引用

页码：1147 / 1155

页数：9

共 50 条

[31] Exact solution of Klein-Gordon equation by asymptotic iteration method
Olgar, Eser
CHINESE PHYSICS LETTERS, 2008, 25 (06) : 1939 - 1942
[32] Arbitrary a""-State Solutions of the Hyperbolical Potential by the Asymptotic Iteration Method
Falaye, B. J.
FEW-BODY SYSTEMS, 2012, 53 (3-4) : 557 - 562
[33] Exact solutions of nonlinear diffusion equations by variational iteration method
Sadighi, A.
Ganji, D. D.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (7-8) : 1112 - 1121
[34] Arbitrary ℓ-State Solutions of the Hyperbolical Potential by the Asymptotic Iteration Method
B. J. Falaye
Few-Body Systems, 2012, 53 : 557 - 562
[35] THE ARNOLDI EIGENVALUE ITERATION WITH EXACT SHIFTS CAN FAIL
Embree, Mark
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2009, 31 (01) : 1 - 10
[36] Variational method for precise asymptotic formulas for nonlinear eigenvalue problems
Shibata T.
Results in Mathematics, 2004, 46 (1-2) : 130 - 145
[37] An adaptive finite element method with asymptotic saturation for eigenvalue problems
C. Carstensen
J. Gedicke
V. Mehrmann
A. Międlar
Numerische Mathematik, 2014, 128 : 615 - 634
[38] An adaptive finite element method with asymptotic saturation for eigenvalue problems
Carstensen, C.
Gedicke, J.
Mehrmann, V.
Miedlar, A.
NUMERISCHE MATHEMATIK, 2014, 128 (04) : 615 - 634
[39] ASYMPTOTIC RATE OF CONVERGENCE OF THE METHOD OF STEEPEST DESCENT IN EIGENVALUE PROBLEMS
ZHUK, PF
USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1984, 24 (02): : 175 - 177
[40] ASYMPTOTIC ANALYSIS AND NUMERICAL METHOD FOR SINGULARLY PERTURBED EIGENVALUE PROBLEMS
Kong, Wang
Huang, Zhongyi
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2018, 40 (05): : A3293 - A3321

← 1 2 3 4 5 →