Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems

Yang, Keqin; Wang, Yingwei; Wu, Xun

doi:10.4208/jcm.1103-m3434

Cited by 13 publications

(9 citation statements)

References 19 publications

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“…is is found using the stability result in eorem 2 and the techniques in [3]. □ Lemma 3 (see [12]). Considering the singularly perturbed reaction-diffusion…”

Section: Proofmentioning

confidence: 99%

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The Novel Rational Spectral Collocation Method for a Singularly Perturbed Reaction-Diffusion Problem with Nonsmooth Data

Lu-feng

2021

Mathematical Problems in Engineering

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A singularly perturbed reaction-diffusion problem with a discontinuous source term is considered. A novel rational spectral collocation combined with a singularity-separated method for this problem is presented. The solution is expressed as u = w + v , where w is the solution of corresponding auxiliary boundary value problem and v is a singular correction with direct expressions. The rational spectral collocation method combined with a sinh transformation is applied to solve the weakened singularly boundary value problem. According to the asymptotic analysis, the sinh transformation parameters can be determined by the width and position of the boundary layers. The parameters in the singular correction can be determined by the boundary conditions of the original problem. Numerical experiment supports theoretical results and shows that compared with previous research results, the novel method has the advantages of a high computational accuracy in singularly perturbed reaction-diffusion problems with nonsmooth data.

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“…is is found using the stability result in eorem 2 and the techniques in [3]. □ Lemma 3 (see [12]). Considering the singularly perturbed reaction-diffusion…”

Section: Proofmentioning

confidence: 99%

“…e parameters of the mapping depend on the position and width of the boundary layer. A rational spectral collocation in a barycentric form with sinh transform (RSC-sinh method) is applied to solve a coupled system of singularly perturbed problems and third-order singularly perturbed problems [11,12].…”

Section: Introductionmentioning

confidence: 99%

The Novel Rational Spectral Collocation Method for a Singularly Perturbed Reaction-Diffusion Problem with Nonsmooth Data

Lu-feng

2021

Mathematical Problems in Engineering

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“…The parameters of the sinh-transform are determined by the width and position of the boundary layer. Chen and Wang [14,15] applied a rational spectral collocation in the barycentric form with sinh-transform to solve a coupled system of singularly perturbed problems and third-order singularly perturbed problems.…”

Section: Introductionmentioning

confidence: 99%

Rational Spectral Collocation Combined with Singularity Separation Method for Second-Order Singular Perturbation Problems

Lu-feng

2023

J Math Sci

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Novel rational spectral collocation is presented in combination with singularity separation method for the second-order singularly perturbed boundary-value problems. The solution is presented in the form u D w C v; where w is the solution of the corresponding third boundary-value problem and v is a singular function with explicit expression. The auxiliary third boundary-value problem is solved by the rational spectral collocation method combined with the asymptotic theory (RSCAT). According to the asymptotic analysis, the parameters of the sinh-transformation can be determined according to the location and width of the boundary layers. The parameters in the singular correction can be determined by the boundary conditions of the original problem. The numerical experiments were carried out to demonstrate the computational efficiency and accuracy of the proposed method.

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“…Lin and Stynes [19] gave a balanced finite element method based on piece-wise quadratic splines for a system of singularly perturbed reaction-diffusion two-point boundary value problems. Also, Chen et al [8] derived collocation method for a coupled system of singularly perturbed linear equations, their method was based on rational spectral collocation method in barycentric form with sinh transform. Clavero et al [9] developed an almost third order finite difference scheme on a piecewise uniform Shishkin mesh for singularly perturbed reaction-diffusion systems.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of a system of singularly perturbed reaction-diffusion problems

Barati

Atabaigi

2019

Filomat

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This paper addresses the numerical approximation of solutions to a coupled system of singularly perturbed reaction-diffusion equations. The components of the solution exhibit overlapping boundary and interior layers. Sinc procedure can control the oscillations in computed solutions at boundary layer regions naturally because the distribution of Sinc points is denser at near the boundaries. Also the obtained results show that the proposed method is applicable even for small perturbation parameter as = 2 −30. The convergence analysis of proposed technique is discussed, it is shown that the approximate solutions converge to the exact solutions at an exponential rate. Numerical experiments are carried out to demonstrate the accuracy and efficiency of the method.

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Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems

Cited by 13 publications

References 19 publications

The Novel Rational Spectral Collocation Method for a Singularly Perturbed Reaction-Diffusion Problem with Nonsmooth Data

The Novel Rational Spectral Collocation Method for a Singularly Perturbed Reaction-Diffusion Problem with Nonsmooth Data

Rational Spectral Collocation Combined with Singularity Separation Method for Second-Order Singular Perturbation Problems

Numerical solutions of a system of singularly perturbed reaction-diffusion problems

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