Iterative method for solving one-dimensional fractional mathematical physics model via quarter-sweep and PAOR
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...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English English |
| Published: |
Springer
2021
|
| Subjects: | |
| Online Access: | https://eprints.ums.edu.my/id/eprint/26832/1/Iterative%20method%20for%20solving%20abstract.pdf https://eprints.ums.edu.my/id/eprint/26832/2/Iterative%20method%20for%20solving.pdf |
| Summary: | 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. |
|---|