Solving the time fractional diffusion equations by the Half-Sweep SOR iterative method

Sunarto, Andang; Sulaiman, Jumat; Saudi, Azali

doi:10.1109/icaicta.2014.7005953

Cited by 6 publications

(5 citation statements)

References 32 publications

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“…Display approximate solutions time. For future works, we will extend this study considering this use of weighted parameter iterative methods [17,18,19,20]…”

Section: Half-sweep Gauss-seidel Iterative Methodsmentioning

confidence: 99%

Numerical Solution for Solving Space-Fractional Diffusion Equations using Half-sweep Gauss-seidel Iterative Method

Sunarto¹,

Sulaiman²,

Saudi³

2015

EECSI

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The main purpose of this paper is to examine the effectiveness of Half-Sweep Gauss-Seidel (HSGS) method for Space-Fractional diffusion equations. The Caputo's derivative and implicit finite difference scheme will be used to discretize linear space-fractional equation of the first order to construct system linear equation. The basic formulation and application of the HSGS iterative method are also presented. Two numerical examples and comparison with other iterative methods shows that the present method is effective. Based on computational numerical result, the solution obtained by proposed iterative method is in excellent agreement, it can be concluded that the proposed iterative method is superior to the Full-Sweep Gauss-Seidel (FSGS) iterative method

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“…Display approximate solutions time. For future works, we will extend this study considering this use of weighted parameter iterative methods [17,18,19,20]…”

Section: Half-sweep Gauss-seidel Iterative Methodsmentioning

confidence: 99%

Numerical Solution for Solving Space-Fractional Diffusion Equations using Half-sweep Gauss-seidel Iterative Method

Sunarto¹,

Sulaiman²,

Saudi³

2015

EECSI

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“…Equation (1) approximates the space-fractional term using the Caputo definition and the second-order half-sweep finite-difference. For more details about half-sweep see [17,[20][21][22]. Suppose that h = l P with P as any positive integer.…”

Section: Approximation To a Space-fractional Diffusion Equationmentioning

confidence: 99%

Approximation Solution of the Fractional Parabolic Partial Differential Equation by the Half-Sweep and Preconditioned Relaxation

et al. 2021

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In this study, the numerical solution of a space-fractional parabolic partial differential equation was considered. The investigation of the solution was made by focusing on the space-fractional diffusion equation (SFDE) problem. Note that the symmetry of an efficient approximation to the SFDE based on a numerical method is related to the compatibility of a discretization scheme and a linear system solver. The application of the one-dimensional, linear, unconditionally stable, and implicit finite difference approximation to SFDE was studied. The general differential equation of the SFDE was discretized using the space-fractional derivative of Caputo with a half-sweep finite difference scheme. The implicit approximation to the SFDE was formulated, and the formation of a linear system with a coefficient matrix, which was large and sparse, is shown. The construction of a general preconditioned system of equation is also presented. This study’s contribution is the introduction of a half-sweep preconditioned successive over relaxation (HSPSOR) method for the solution of the SFDE-based system of equation. This work extended the use of the HSPSOR as an efficient numerical method for the time-fractional diffusion equation, which has been presented in the 5th North American International Conference on industrial engineering and operations management in Detroit, Michigan, USA, 10–14 August 2020. The current work proposed several SFDE examples to validate the performance of the HSPSOR iterative method in solving the fractional diffusion equation. The outcome of the numerical investigation illustrated the competence of the HSPSOR to solve the SFDE and proved that the HSPSOR is superior to the standard approximation, which is the full-sweep preconditioned SOR (FSPSOR), in terms of computational complexity.

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“…However, this study don't use the operator 7which is shown as the full-sweep Caputo's fractional derivative since this study focus to the half-sweep concept. Refer to the study of Sonarto et al [17] over the problem, we have propose the half-sweep concept to the Caputo's fractional derivative operator based on the operator (7) as follows:…”

Section: Half-sweep Approximation Equationmentioning

confidence: 99%

Application of The Half-Sweep Egsor Iteration for Two-Point Boundary Value Problems of Fractional Order

Rahman¹,

Ali²,

Sulaiman³

et al. 2019

Adv. sci. technol. eng. syst. j.

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The point of this study is to explore and elucidating the performance of the four-point Half-Sweep EGSOR (4HSEGSOR) iterative method to solve fractional two-point boundary value problems by using Caputo's fractional operator and family of finite differences (FD) schemes. To apply the iterative methods, linear system needs to be constructed via the discretization process with fractional order to get the approximation equation of the linear fractional two point boundary value problem by using the Caputo's derivative operator. Then the generated linear system has been solved using the proposed 4HSEGSOR iterative method. In the addition, the formulation and application of the 4HSEGSOR method to solve the problems are also presented. Three numerical examples and comparison are used to illustrate with tested FSSOR and HSSOR methods. The numerical results reveals the effectiveness of 4HSEGSOR method compared with tested iterative methods.

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Solving the time fractional diffusion equations by the Half-Sweep SOR iterative method

Cited by 6 publications

References 32 publications

Numerical Solution for Solving Space-Fractional Diffusion Equations using Half-sweep Gauss-seidel Iterative Method

Numerical Solution for Solving Space-Fractional Diffusion Equations using Half-sweep Gauss-seidel Iterative Method

Approximation Solution of the Fractional Parabolic Partial Differential Equation by the Half-Sweep and Preconditioned Relaxation

Application of The Half-Sweep Egsor Iteration for Two-Point Boundary Value Problems of Fractional Order

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