Efficiency Evaluation of Half-Sweep Newton-EGSOR Method to Solve 1D Nonlinear Porous Medium Equations

Chew, Jackel Vui Lung; Aruchunan, Elayaraja; Sulaiman, Jumat

doi:10.1007/978-3-030-79606-8_25

Cited by 2 publications

(2 citation statements)

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“…The method was found to be unconditionally stable, having fourth-order and second-order accuracy with respect to space-time, respectively. Recently, Chew et al, [26] applied the Half-sweep Newton Successive Over Relaxation numerical method for dealing with a 1D non-linear porous medium equation. The authors found that their method gave an unconditionally stable solution and, hence, was a suitable numerical method for non-linear partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Axial Groundwater Contaminant Dispersion Modeling for a Finite Heterogeneous Porous Medium

Radha

Singh

2023

Water

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In this study, a two-dimensional contaminant transport model with time-varying axial input sources subject to non-linear sorption, decay, and production is numerically solved to find the concentration distribution profile in a heterogeneous, finite soil medium. The axial input sources are assigned on the coordinate axes of the soil medium, with background sources varying sinusoidally with space. The groundwater velocities are considered space-dependent in the longitudinal and transversal directions. Various forms of axial input sources are considered to study their transport patterns in the medium. The alternating direction implicit (ADI) and Crank-Nicolson (CN) methods are applied to approximate the two-dimensional governing equation, and the obtained algebraic system of equations in each case is further solved by MATLAB scripts. Both approximate solutions are illustrated graphically for various hydrological input data. The influence of various hydrogeological input parameters, such as the medium’s porosity, density, sorption conditions, dispersion coefficients, etc., on the contaminant distribution is analyzed. Further, the influence of constant and varying velocity parameters on groundwater contaminant transport is studied. The stability of the proposed model is tested using the Peclet and Courant numbers. Substantial similarity is observed when the approximate solution obtained using the CN method is compared with the finite element method in a special case. The proposed approximate solution is compared with the existing numerical solutions, and an overall agreement of 98–99% is observed between them. Finally, the stability analysis reveals that the model is stable and robust.

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Section: Introductionmentioning

confidence: 99%

Axial Groundwater Contaminant Dispersion Modeling for a Finite Heterogeneous Porous Medium

Radha

Singh

2023

Water

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“…Several applications of the halfsweep iteration have been carried out in solving integral equations in [18][19][20]. Besides that, it is also found in solving fractional diffusion [21], reaction-diffusion equations [22], porous medium equations [23], Burger's equations [24], and Fredholm integro-differential equations [25]. Based on these studies, it has demonstrated that the key concept of the half-sweep iteration is to take just half of the total number of node points of the problem from the solution domain.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Nonlinear Fredholm Integral Equations Using Half-Sweep Newton-PKSOR Iteration

Ali¹,

Sulaiman²,

Saudi³

et al. 2022

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This paper is concerned with producing an efficient numerical method to solve nonlinear Fredholm integral equations using Half-Sweep Newton-PKSOR (HSNPKSOR) iteration. The computation of numerical methods in solving nonlinear equations usually requires immense amounts of computational complexity. By implementing a Half-Sweep approach, the complexity of the calculation is tried to be reduced to produce a more efficient method. For this purpose, the steps of the solution process are discussed beginning with the derivation of nonlinear Fredholm integral equations using a quadrature scheme to get the half-sweep approximation equation. Then, the generated approximation equation is used to develop a nonlinear system. Following that, the formulation of the HSNPKSOR iterative method is constructed to solve nonlinear Fredholm integral equations. To verify the performance of the proposed method, the experimental results were compared with the Full-Sweep Newton-KSOR (FSNKSOR), Half-Sweep Newton-KSOR (HSNKSOR), and Full-Sweep Newton-PKSOR (FSNPKSOR) using three parameters: number of iteration, iteration time, and maximum absolute error. Several examples are used in this study to illustrate the efficiency of the tested methods. Based on the numerical experiment, the results appear that the HSNPKSOR method is effective in solving nonlinear Fredholm integral equations mainly in terms of iteration time compared to rest tested methods.

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Efficiency Evaluation of Half-Sweep Newton-EGSOR Method to Solve 1D Nonlinear Porous Medium Equations

Cited by 2 publications

References 30 publications

Axial Groundwater Contaminant Dispersion Modeling for a Finite Heterogeneous Porous Medium

Axial Groundwater Contaminant Dispersion Modeling for a Finite Heterogeneous Porous Medium

Numerical Solution of Nonlinear Fredholm Integral Equations Using Half-Sweep Newton-PKSOR Iteration

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