Open AccessFour-Point EGSOR Iteration for the Grünwald Implicit Finite Difference Solution of One-Dimensional Time-Fractional Parabolic Equations
Author(s) -
Fatihah Anas Muhiddin,
Jumat Sulaiman,
Andang Sunarto
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1366/1/012086
Subject(s) - mathematics , discretization , alternating direction implicit method , successive over relaxation , iterative method , relaxation (psychology) , operator (biology) , gauss–seidel method , finite difference , finite difference method , derivative (finance) , mathematical analysis , mathematical optimization , local convergence , psychology , social psychology , biochemistry , chemistry , repressor , transcription factor , gene , financial economics , economics
In this paper, our main concerned is on the application of the formulation of a four-point explicit group successive over-relaxation (4EGSOR) iterative method in solving one-dimensional time-fractional parabolic equations based on the second-order Grünwald implicit approximation equation. The formulation of the 4EGSOR method is constructed by using the implicit approximation equation which is derived by the Grunwald derivative operator and the implicit finite difference discretization scheme. In order to access the performance results of the 4EGSOR iterative method, another block and point iterative methods which are the four-point EGGS (4EGGS) and the Gauss-Seidel (GS) were also presented as control methods. The results of three numerical experiments show substantial improvement in terms of the number of iterations and execution time.