Chebyshev spectral-SN method for the neutron transport equation

Asadzadeh, Mohammad; Kadem, Abdelouahab

doi:10.1016/j.camwa.2005.11.039

Cited by 21 publications

(9 citation statements)

References 11 publications

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“…If v 0 is infinitive, then we say the multistep method to be P-stable. Based on the definition of interval of periodicity, we firstly assume all the characteristic roots of (11) to have the following form…”

Section: The Necessary Conditions For a P-stable Multistep Methodsmentioning

confidence: 99%

A new high order implicit four-step methods with vanished phase-lag and some of its derivatives for the numerical solution of the radial Schr¨odinger equation

Shokri

Tahmourasi²

2017

J. of Mod. Meth. in Numer. Math.

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A new four-step implicit linear eight algebraic order method with vanished phase-lag and its first, second and third derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schrödinger equation and related problems. In order to produce an efficient multistep method the phase-lag property and its derivatives are used. An error analysis and a stability analysis is also investigated and a comparison with other methods is also studied. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.

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Section: The Necessary Conditions For a P-stable Multistep Methodsmentioning

confidence: 99%

A new high order implicit four-step methods with vanished phase-lag and some of its derivatives for the numerical solution of the radial Schr¨odinger equation

Shokri

Tahmourasi²

2017

J. of Mod. Meth. in Numer. Math.

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“…The literature on the topic is quite extensive and hence can not be described here in detail. However, some works of eminent researchers regarding the transport model have been presented in the [4][5][6][7][8][9][10]. Literature survey indicates that very little attention has been given to the fractional neutron transport equation.…”

Section: Introductionmentioning

confidence: 99%

A novel simulation methodology of fractional order nuclear science model

Akgül

Khan

2017

Math Methods in App Sciences

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In this paper, a novel simulation methodology based on the reproducing kernels is proposed for solving the fractional order integro‐differential transport model for a nuclear reactor. The analysis carried out in this paper thus forms a crucial step in the process of development of fractional calculus as well as nuclear science models. The fractional derivative is described in the Captuo Riemann–Liouville sense. Results are presented graphically and in tabulated forms to study the efficiency and accuracy of method. The present scheme is very simple, effective, and appropriate for obtaining numerical simulation of nuclear science models. Copyright © 2017 John Wiley & Sons, Ltd.

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“…In the present paper we present a new approximation for the one dimensional transport equation, using Chebyshev polynomials [1] combined with the Sumudu transform.…”

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confidence: 99%