2024, Vol. 5, Issue 2, Part B
Iterative method for solving fractional mathematical physics model
Author(s): Mahesh T Holambe and Vinod B Kulkarni
Abstract: 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 coefficient 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 solution’s 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 method. 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.
DOI: https://doi.org/10.22271/math.2024.v5.i2b.157
Pages: 106-113 | Views: 54 | Downloads: 13
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How to cite this article:
Mahesh T Holambe and Vinod B Kulkarni. Iterative method for solving fractional mathematical physics model. Journal of Mathematical Problems, Equations and Statistics. 2024; 5(2): 106-113. DOI: 10.22271/math.2024.v5.i2b.157
