Solution of One-Dimensional Porous Medium Equation Using Half-Sweep Newton-MSOR Iteration

Chew, Jackel Vui Lung; Sulaiman, Jumat

doi:10.1166/asl.2018.11186

Cited by 4 publications

(4 citation statements)

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“…As mentioned in section 2, the iterative method namely SOR is applied with combination of HS concept to solve the sparse linear system (10). The HS iteration concept is known as the complexity reduction approach [15] which is introduced by Abdullah [16]. Due to its advantage, many authors have been attracted to use the applications of the HS iteration concept in solving the numerical issues in their research [17][18][19][20].…”

Section: Formulation Of Half-sweep Sor Iterationmentioning

confidence: 99%

“…The HS iteration concept is known as the complexity reduction approach [15] which is introduced by Abdullah [16]. Due to its advantage, many authors have been attracted to use the applications of the HS iteration concept in solving the numerical issues in their research [17][18][19][20]. Therefore, the corresponding sparse linear system (10) also has been solved by using the HS iteration concept via the SOR method since the SOR method is the common option for efficient solution.…”

Section: Formulation Of Half-sweep Sor Iterationmentioning

confidence: 99%

“…Consider the following PDE which is found in many transport phenomena (15) with the initial condition…”

Section: Example 2 [25]mentioning

confidence: 99%

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

Ali

Rahman

Sulaiman

et al. 2019

IJEECS

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<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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Section: Formulation Of Half-sweep Sor Iterationmentioning

confidence: 99%

Section: Formulation Of Half-sweep Sor Iterationmentioning

confidence: 99%

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

Ali

Rahman

Sulaiman

et al. 2019

IJEECS

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show abstract

“…Due to the potential of the HSMSOR method, [15,16] applied the method to simulate indoor mobile robots' path planning and agent navigations, respectively. Since nonlinear problems are more realistic to be solved, [17] initiated the investigation of solving one-dimensional NPPDE using their HSMSOR method.…”

Section: Introductionmentioning

confidence: 99%

Half-sweep Modified SOR Approximation of A Two-dimensional Nonlinear Parabolic Partial Differential Equation

Chew¹,

Sulaiman²,

Sunarto³

et al. 2023

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The sole subject of this numerical analysis was the half-sweep modified successive over-relaxation approach (HSMSOR), which takes the form of an iterative formula. This study computed a class of two-dimensional nonlinear parabolic partial differential equations subject to Dirichlet boundary conditions numerically using the implicit-type finite difference scheme. The computational cost optimization was considered by converting the traditional implicit finite difference approximation into the half-sweep finite difference approximation. The implementation required inner-outer iteration cycles, the second-order Newton method, and a linearization technique. The created HSMSOR is utilized to obtain an approximation of the linearized equations system through the inner iteration cycle. In contrast, the problem's numerical solutions are obtained using the outer iteration cycle. The study examined the local truncation error and the stability, convergence, and method analysis. Results from three initial-boundary value issues showed that the proposed method had competitive computational costs compared to the existing method.

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Efficient Iterative Approximation for Nonlinear Porous Medium Equation with Drainage Model

Chew

Sulaiman

Aruchunan

et al. 2022

Studies in Systems, Decision and Control

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Solution of One-Dimensional Porous Medium Equation Using Half-Sweep Newton-MSOR Iteration

Cited by 4 publications

References 0 publications

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

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

Half-sweep Modified SOR Approximation of A Two-dimensional Nonlinear Parabolic Partial Differential Equation

Efficient Iterative Approximation for Nonlinear Porous Medium Equation with Drainage Model

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