Implicit finite difference solution for time-fractional diffusion equations using AOR method

Sunarto, Andang; Sulaiman, Jumat; Saudi, Azali

doi:10.1088/1742-6596/495/1/012032

Cited by 22 publications

(13 citation statements)

References 21 publications

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“…This indicates that the non-polynomial spline scheme together with the SOR method can cope with the accumulated round-off error better than GS method. Thus, For future work, it is highly recommended to extend this study for solving high order two-point BVPs with different degree of spline such as quartic, quintic and so on by referring to [1][2][3][4][5], [14][15]22]. …”

Section: Resultsmentioning

confidence: 99%

“…By using computer program, Equation (14) was used to construct a system of linear equations in a matrix form of Equation Equation (15) …”

Section: Methods Of Solutionmentioning

confidence: 99%

“…1 of each subinterval is given as follows Then, Equation (3) and (5) were solved iteratively at once by using SOR iter referring to [12][13][14][15]. In order to assess the performance of this proposed idea clearly in term of iterations number, execution time and maximum absolute error, GS iterative method was also conducted for comparison purpose.…”

Section: H Justine Et Almentioning

confidence: 99%

“…To do this, the first system was first iterated to get the value of function G(x) which then passed to the second system in order to solve it. Even though these two linear systems were solved differently, but both still using the same general approximation Equation (14). The algorithm of the SOR iteration when solving the two systems of linear equations are presented in Table 1.…”

Section: Algorithmmentioning

confidence: 99%

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Solution of fourth-order two-point BVPs with cubic non-polynomial spline and SOR iterative method

Justine

Sulaiman

2018

J. Fundam and Appl Sci.

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Two-point boundary value problems (BVPs) have numerous applications especially in the modeling of most physical phenomena. In this study, the fourth order two solved by using Successive Over cubic non-polynomial spline scheme a numerical experiment was conducted method and the spline scheme in terms of iterations number, execution time and maximum absolute error at different mesh sizes idea, another iterative method was also conducted which is Gauss numerical analysis, the two-point BVPs scheme were found to be best solved by point boundary value problems (BVPs) have numerous applications especially in the modeling of most physical phenomena. In this study, the fourth order two-point BVPs were using Successive Over-Relaxation (SOR) iterative method after discretized with lynomial spline scheme to generate its corresponding sparse linear system. Then, was conducted to determine the performances of the SOR itera the spline scheme in terms of iterations number, execution time and maximum absolute error at different mesh sizes. In order to assess the performances of this proposed idea, another iterative method was also conducted which is Gauss-Seidel (GS).point BVPs together with the cubic non-polynomial spline solved by using the SOR iterative method.

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Section: Resultsmentioning

confidence: 99%

“…By using computer program, Equation (14) was used to construct a system of linear equations in a matrix form of Equation Equation (15) …”

Section: Methods Of Solutionmentioning

confidence: 99%

Section: H Justine Et Almentioning

confidence: 99%

Section: Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

Solution of fourth-order two-point BVPs with cubic non-polynomial spline and SOR iterative method

Justine

Sulaiman

2018

J. Fundam and Appl Sci.

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“…Clearly there is a general formula for arbitrary r in terms of the cofactors of A. In particular, it can be fitted into the framework of linear sequential FDEs [16,20,21,22,23]. These take the form…”

Section: The Solution Of Mixed Index Linear Systemsmentioning

confidence: 99%

On the Analysis of Mixed-Index Time Fractional Differential Equation Systems

Burrage¹,

Burrage²,

Turner³

et al. 2018

Preprint

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In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalised Mittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.

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Implementation of the 4EGKSOR for Solving One-Dimensional Time-Fractional Parabolic Equations with Grünwald Implicit Difference Scheme

Muhiddin

Sulaiman

Sunarto

2020

Lecture Notes in Electrical Engineering

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Implicit finite difference solution for time-fractional diffusion equations using AOR method

Cited by 22 publications

References 21 publications

Solution of fourth-order two-point BVPs with cubic non-polynomial spline and SOR iterative method

Solution of fourth-order two-point BVPs with cubic non-polynomial spline and SOR iterative method

On the Analysis of Mixed-Index Time Fractional Differential Equation Systems

Implementation of the 4EGKSOR for Solving One-Dimensional Time-Fractional Parabolic Equations with Grünwald Implicit Difference Scheme

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