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This paper will solve one of the fractional mathematical physics models, a one-dimensional time-fractional differential equation, by utilizing the second-order quarter-sweep finite-difference scheme and the preconditioned accelerated over-relaxation method. The proposed numerical method offers an efficient solution to the time-fractional differential equation by applying the computational complexity reduction approach by the quarter-sweep technique. The finite-difference approximation equation will be formulated based on the Caputo’s time-fractional derivative and quarter-sweep central difference in space. The developed approximation equation generates a linear system on a large scale and has sparse coefficients. With the quarter-sweep technique and the preconditioned iterative method, computing the time-fractional differential equation solutions can be more efficient in terms of the number of iterations and computation time. The quarter-sweep computes a quarter of the total mesh points using the preconditioned iterative method while maintaining the solutions’ accuracy. A numerical example will demonstrate the efficiency of the proposed quarter-sweep preconditioned accelerated over-relaxation method against the half-sweep preconditioned accelerated over-relaxation, and the full-sweep preconditioned accelerated over-relaxation methods. The numerical finding showed that the quarter-sweep finite difference scheme and preconditioned accelerated over-relaxation method can serve as an efficient numerical method to solve fractional differential equations.

The purpose of this paper is to see the impact of social media on the idea of radicalism. In writing this paper using literature study method. And from the description in this paper can be concluded that social media have a positive and  negative impact. The negative impact of the free use of social media is the ease of accepting the Indonesian public receiving information including radicalism from all fields without finding out the truth of this information.

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We investigate the application of Quarter-Sweep Gauss-Seidel (QSGS) iterative method for solving (SFPDE’s) space-fractional partial diffusion equations with Dirichlet boundary condition. To do this, implicit finite difference scheme and Caputo’s derivative operator are used to discretize one-dimensional linear space-fractional equation to form system of linear equations. Then basic ideas formulation and application of the suggested iterative method are also introduced. Numerical examples of tested problems were carried out to demonstrate advantages of the proposed iterative method beside to the HSGS and FSGS as control method. Based on computational results, the QSGS method is shown to be the most superior than the HSGS and FSGS iterative methods.