Iterative methods for solving space-time one dimensional multigroup diffusion equations

2010 ◽  
Vol 5 (2) ◽  
pp. 114
Author(s):  
Y. Yulianti ◽  
Z. Su'ud ◽  
A. Waris ◽  
S.N. Khotimah
Keyword(s):  
Iterative Methods ◽  
Space Time ◽  
Diffusion Equations ◽  
One Dimensional

Analytical solutions of the space–time fractional Telegraph and advection–diffusion equations

2018 ◽  
Vol 491 ◽  
pp. 810-819 ◽  
Author(s):  
Ashraf M. Tawfik ◽  
Horst Fichtner ◽  
Reinhard Schlickeiser ◽  
A. Elhanbaly
Keyword(s):  
Analytical Solutions ◽  
Space Time ◽  
Diffusion Equations ◽  
Advection Diffusion

scholarly journals A space-time adaptive method for reservoir flows: formulation and one-dimensional application

2017 ◽  
Vol 22 (1) ◽  
pp. 107-123 ◽  
Author(s):  
Savithru Jayasinghe ◽  
David L. Darmofal ◽  
Nicholas K. Burgess ◽  
Marshall C. Galbraith ◽  
Steven R. Allmaras
Keyword(s):  
Adaptive Method ◽  
Space Time ◽  
One Dimensional

scholarly journals Solutions of reaction-diffusion equations using similarity reduction and HSSOR iteration

2019 ◽  
Vol 16 (3) ◽  
pp. 1430
Author(s):  
Nur Afza Mat Ali ◽  
Rostang Rahman ◽  
Jumat Sulaiman ◽  
Khadizah Ghazali
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Iterative Method ◽  
Iterative Methods ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Sparse Linear System ◽  
Successive Over Relaxation ◽  
Number Of Iterations

<p>Similarity method is used in finding the solutions of partial differential equation (PDE) in reduction to the corresponding ordinary differential equation (ODE) which are not easily integrable in terms of elementary or tabulated functions. Then, the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is applied in solving the sparse linear system which is generated from the discretization process of the corresponding second order ODEs with Dirichlet boundary conditions. Basically, this ODEs has been constructed from one-dimensional reaction-diffusion equations by using wave variable transformation. Having a large-scale and sparse linear system, we conduct the performances analysis of three iterative methods such as Full-sweep Gauss-Seidel (FSGS), Full-sweep Successive Over-Relaxation (FSSOR) and HSSOR iterative methods to examine the effectiveness of their computational cost. Therefore, four examples of these problems were tested to observe the performance of the proposed iterative methods.  Throughout implementation of numerical experiments, three parameters have been considered which are number of iterations, execution time and maximum absolute error. According to the numerical results, the HSSOR method is the most efficient iterative method in solving the proposed problem with the least number of iterations and execution time followed by FSSOR and FSGS iterative methods.</p>

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