Explicit group iterative methods for the solution of two-dimensional time-fractional telegraph equation

On Unconditionally Stable New Modified Fractional Group Iterative Scheme for the Solution of 2D Time-Fractional Telegraph Model

“…The lin f ty norm was utilized for the convergence criterion, with a factor of ε = 10 The numerical results in Table 1 and 2 are obtained using the FSP, FEG, and MFEG iterative methods in terms of elapsed time (in seconds), number of iterations, average absolute error, and maximum absolute error. The fractional standard point (FSP) and fractional explicit group (FEG) iterative schemes are derived in [6] for 2D fractional telegraph equation. Graphs of execution time and iteration count are illustrated in Figures 1 and 2 Example 1.…”

“…The h-spaced point and group iterative schemes for 2D fractional telegraph equation have been derived by Ali and Ali in [6]. The following standard 2h-spaced iterative scheme can be obtain by utilizing standard 2h-spaced Crank-Nicolson scheme for space-derivatives and Caputo fractional derivatives from Equations (4) and (5) for time-derivatives in Equation (2), we have the following expression,…”

“…Partial differential equations have a wide range of applications in applied sciences, including wave propagation, electric signal propagation, and atomic physics [1][2][3][4][5]. In recent years, several numerical techniques for multidimensional hyperbolic partial differential equations have been developed [6][7][8][9][10][11]. For example, Gao and Chi [12] solved one-spacedimensional linear hyperbolic model based on unconditionally stable difference schemes.…”

A Modified Accelerated Overrelaxation (Maor) Scheme for Solving the Shifted Gr\"{u}nwald Estimation Fractional Poisson Equation

“…Furthermore, some time-fractional diffusion equations [4,9,43] and space-fractional diffusion equations [33,34,35] have sometimes been solved using various sweeping iterative methods. Another equation includes the two-dimensional time-fractional telegraph equation which has been solved on the rotated iterative method [5] and by utilizing the explicit group iterative method [3].…”

New group iterative schemes for solving the two-dimensional anomalous fractional sub-diffusion equation

“…In this case, the preliminary work has been done by Balasim and Ali (2016-17) [10][11][12] on two-dimensional timefractional diffusion and advection-diffusion PDEs, by utilizing Caputo's fractional derivative, where the time-fractional derivative of order α lies between 0 and 1. In addition, the most recent work by Ali and Ali (2018-19) [3][4][5] on two-dimensional time-fractional wave, damped wave and hyperbolic telegraph PDEs, by using the same definition of Caputo's fractional derivative, where the order of time-fractional derivative α ∈ (1, 2). In this paper, we step forward towards the numerical solution of more complicated 2D timefractional anomalous sub-diffusion equation by applying by Riemann-Liouville fractional derivative and grouping methods, and results were found according to our expectation.…”