Browsing by Author "Taneja, 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: 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.