Quasilinearization approach to computations with singular potentials

Krivec, R.; Mandelzweig, V. B.

doi:10.1016/j.cpc.2008.07.006

Cited by 22 publications

(5 citation statements)

References 49 publications

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“…1 it is obvious that even in our extreme singular example, precision of the order of 20 digits in E is achieved with only four QLM iterations, like in previous work [2,14]. Because of this, we again usually fix M to values 4; 8; 12; .…”

Section: Convergence Of Ementioning

confidence: 85%

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Unified QLM for regular and arbitrary singular potentials

Krivec

2014

Applied Mathematics and Computation

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Section: Convergence Of Ementioning

confidence: 85%

“…Our numerical implementation for the radial Schrödinger equation [14,17,18,21], for easier handling of nodes in the radial solution vðrÞ, uses the (negative) form of solution:…”

Section: The Qlm Approachmentioning

confidence: 99%

Unified QLM for regular and arbitrary singular potentials

Krivec

2014

Applied Mathematics and Computation

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“…The quasi-linearization method (QLM) based on the Newton-Raphson method has introduced by Bellman and Kalaba [32,33]. Some researchers have used this method in their works [34,35,36,37].…”

Section: The Methodologymentioning

confidence: 99%

An efficient numerical method for solving nonlinear Thomas-Fermi equation

Parand

Rabiei

Delkhosh

2018

Acta Universitatis Sapientiae, Mathematica

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In this paper, the nonlinear Thomas-Fermi equation for neutral atoms by using the fractional order of rational Chebyshev functions of the second kind (FRC2), ${\rm{FU}}_{\rm{n}}^\alpha \left( {{\rm{t}},{\rm{L}}} \right)$ (t, L), on an unbounded domain is solved, where L is an arbitrary parameter. Boyd (Chebyshev and Fourier Spectral Methods, 2ed, 2000) has presented a method for calculating the optimal approximate amount of L and we have used the same method for calculating the amount of L. With the aid of quasilinearization and FRC2 collocation methods, the equation is converted to a sequence of linear algebraic equations. An excellent approximation solution of y(t), y′ (t), and y ′ (0) is obtained.

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“…The quasilinearization method [11][12][13] can be considered as an example for iteration methods. Its fast convergence, 2 Mathematical Problems in Engineering monotonicity, and numerical stability were analyzed by Krivec and Mandelzweig [12].…”

Section: Recent Workmentioning

confidence: 99%

Bernstein Series Solution of a Class of Lane-Emden Type Equations

Işık

Sezer

2013

Mathematical Problems in Engineering

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The purpose of this study is to present an approximate solution that depends on collocation points and Bernstein polynomials for a class of Lane-Emden type equations with mixed conditions. The method is given with some priori error estimate. Even the exact solution is unknown, an upper bound based on the regularity of the exact solution will be obtained. By using the residual correction procedure, the absolute error can be estimated. Also, one can specify the optimal truncation limitnwhich gives a better result in any norm. Finally, the effectiveness of the method is illustrated by some numerical experiments. Numerical results are consistent with the theoretical results.

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Quasilinearization approach to computations with singular potentials

Cited by 22 publications

References 49 publications

Unified QLM for regular and arbitrary singular potentials

Unified QLM for regular and arbitrary singular potentials

An efficient numerical method for solving nonlinear Thomas-Fermi equation

Bernstein Series Solution of a Class of Lane-Emden Type Equations

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