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Design and stability analysis of an implicit non-standard finite difference scheme for fractional neutron point kinetic equation

Publication Type : Journal Article

Publisher : North-Holland

Source : North-Holland

Campus : Coimbatore

School : School of Engineering

Center : Amrita Innovation & Research

Department : Mathematics

Verified : Yes

Year : 2019

Abstract : This paper is concerned with the construction of a new numerical technique to obtain approximate solution for an extended fractional neutron point kinetic (EFNPK) model with six groups of delayed neutron precursors. The fractional derivative is approximated by means of Caputo's definition and the shifted Grünwald-Letnikov formula is used to obtain a finite difference approximation for the solution of this model. The discretization leads to an implicit finite difference scheme. The stability analysis of the method is discussed. It is proved that the method is unconditionally stable. Various numerical experiments are carried out for validity and efficiency of the suggested method. The neutron density is calculated for three types of reactivity: step, ramp and sinusoidal reactivity. The influences of anomalous diffusion exponent, reactivity functions, relaxation time and time steps on the neutron density are examined. Comparison is made between the results corresponding to the EFNPK model [4] and the results corresponding to the fractional neutron point kinetic model proposed in [17]. Comparison confirms that the difference between the values of neutron density increases as the anomalous diffusion exponent decreases or computational time increases. Comparison is also made between the approximate solution obtained by the suggested method and exact solution of the classical model for step and ramp reactivity. Moreover, our results are compared with those obtained by other methods.

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