Browsing by Author "Majeed, Abdul"

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Citation - WoS: 25
Citation - Scopus: 22
Numerical Approximation of Inhomogeneous Time Fractional Burgers-Huxley Equation With B-Spline Functions and Caputo Derivative
(Springer, 2022) Kamran, Mohsin; Asghar, Noreen; Baleanu, Dumitru; Majeed, Abdul
A prototype model used to explain the relationship between mechanisms of reaction, convection effects, and transportation of diffusion is the generalized Burgers-Huxley equation. This study presents numerical solution of non-linear inhomogeneous time fractional Burgers-Huxley equation using cubic B-spline collocation method. For this purpose, Caputo derivative is used for the temporal derivative which is discretized by L1 formula and spatial derivative is interpolated with the help of B-spline basis functions, so the dependent variable is continuous throughout the solution range. The validity of the proposed scheme is examined by solving four test problems with different initial-boundary conditions. The algorithm for the execution of scheme is also presented. The effect of non-integer parameter alpha and time on dependent variable is studied. Moreover, convergence and stability of the proposed scheme is analyzed, and proved that scheme is unconditionally stable. The accuracy is checked by error norms. Based on obtained results we can say that the proposed scheme is a good addition to the existing schemes for such real-life problems.
Citation - WoS: 58
Citation - Scopus: 61
Solving Time Fractional Burgers' and Fisher's Equations Using Cubic B-Spline Approximation Method
(Springer, 2020) Kamran, Mohsin; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Majeed, Abdul
This article presents a numerical algorithm for solving time fractional Burgers' and Fisher's equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank-Nicolson scheme based on cubic B-spline functions is used to interpolate the solution curve along the spatial grid. The numerical scheme has been implemented on three test problems. The obtained results indicate that the proposed method is a good option for solving nonlinear fractional Burgers' and Fisher's equations. The error norms L2 and L infinity have been calculated to validate the efficiency and accuracy of the presented algorithm.