Browsing by Author "Chawla, Reetika"

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Citation - WoS: 20
A Novel Finite Difference Based Numerical Approach for Modified Atangana-Baleanu Caputo Derivative
(Amer inst Mathematical Sciences-aims, 2022) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Chawla, Reetika
In this paper, a new approach is presented to investigate the time-fractional advection-dispersion equation that is extensively used to study transport processes. The present modified fractional derivative operator based on Atangana-Baleanu's definition of a derivative in the Caputo sense involves singular and non-local kernels. A numerical approximation of this new modified fractional operator is provided and applied to an advection-dispersion equation. Through Fourier analysis, it has been proved that the proposed scheme is unconditionally stable. Numerical examples are solved that validate the theoretical results presented in this paper and ensure the proficiency of the numerical scheme.
Citation - WoS: 2
Numerical Investigation of Two Fractional Operators for Time Fractional Delay Differential Equation
(Springer, 2024) Chawla, Reetika; Kumar, Devendra; Baleanu, Dumitru
This article compared two high-order numerical schemes for convection-diffusion delay differential equation via two fractional operators with singular kernels. The objective is to present two effective schemes that give (3-alpha)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(3-\alpha )$$\end{document} and second order of accuracy in the time direction when alpha is an element of(0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in (0,1)$$\end{document} using Caputo and Modified Atangana-Baleanu Caputo derivatives, respectively. We also implemented a trigonometric spline technique in the space direction, giving second order of accuracy. Moreover, meticulous analysis shows these numerical schemes to be unconditionally stable and convergent. The efficiency and reliability of these schemes are illustrated by numerical experiments. The tabulated results obtained from test examples have also shown the comparison of these operators.
Citation - WoS: 8
Citation - Scopus: 9
Numerical Simulation for Generalized Time-Fractional Burgers' Equation With Three Distinct Linearization Schemes
(Asme, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Chawla, Reetika
In the present study, we examined the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative by adopting the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also presented. All linearization strategies used to solve the proposed nonlinear problem are unconditionally stable. To support the theory, two numerical examples are considered. Furthermore, numerical results demonstrate the comparison of linearization strategies and manifest the effectiveness of the proposed numerical scheme in three distinct ways.