Browsing by Author "Deswal, Komal"

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Citation Count: Taneja, Komal...et al. (2023). "A Higher-Order Approach For Time-Fractional Generalized Burgers' Equation", Fractals-Complex Geometry Patterns And Scaling In Nature And Society, Vol.31, No.07
A Higher-Order Approach For Time-Fractional Generalized Burgers' Equation
(2023) Taneja, Komal; Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; 56389
A fast higher-order scheme is established for solving inhomogeneous time-fractional generalized Burgers' equation. The time-fractional operator is taken as the modified operator with the Mittag-Leffler kernel. Through stability analysis, it has been demonstrated that the proposed numerical approach is unconditionally stable. The convergence of the numerical method is analyzed theoretically using von Neumann's method. It has been proved that the proposed numerical method is fourth-order convergent in space and second-order convergent in time in the L-2-norm. The scheme's proficiency and effectiveness are examined through two numerical experiments to validate the theoretical estimates. The tabular and graphical representations of numerical results confirm the high accuracy and versatility of the scheme.
Citation Count: Chawla, Reetika;...et.al. (2022). "A novel finite difference based numerical approach for Modified Atangana-Baleanu Caputo derivative", AIMS Mathematics, Vol.7, No.9, pp.17252-17268.
A novel finite difference based numerical approach for Modified Atangana-Baleanu Caputo derivative
(2022) Chawla, Reetika; Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; 56389
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 Count: Taneja, Komal;...et.al. (2023). "Novel Numerical Approach for Time Fractional Equations with Nonlocal Condition", Numerical Algorithms.
Novel Numerical Approach for Time Fractional Equations with Nonlocal Condition
(2023) Taneja, Komal; Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; 56389
A numerical method for solving inhomogeneous nonlocal time fractional convection-diffusion-reaction equations with variable coefficients has been developed. The fractional time operator is taken in the sense of the modified operator with the Mittag-Leffler kernel. The numerical method is based on the modified Gauss elimination with Taylor’s expansion. Through rigorous analysis, it has been proved that the given method is unconditionally stable and second-order convergent in space and time. The numerical results for three test problems illustrate the efficiency and validity of the theoretical estimates.
Citation Count: Reetika, Chawla;...et.al. (2023). "Numerical Simulation for Generalized Time-Fractional Burgers Equation With Three Distinct Linearization Schemes", Journal of Computational and Nonlinear Dynamics, Vol.18, No.4.
Numerical Simulation for Generalized Time-Fractional Burgers Equation With Three Distinct Linearization Schemes
(2023) Reetika, Chawla; Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; 56389
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. © 2023 American Society of Mechanical Engineers (ASME).