Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction–diffusion boundary-value problems

Das, P. C.; Natesan, Srinivasan

doi:10.1016/j.amc.2014.10.023

Cited by 51 publications

(20 citation statements)

References 24 publications

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“…The convergence is first order accurate. The present analysis generalizes the results obtained in earlier publications [8,9].…”

supporting

confidence: 91%

“…We use the adaptive moving mesh methods [6] which start with a fixed number of mesh points and produce a layer adapted mesh by a iterative technique. The present method is based on the idea of equidistribution which is investigated in [2] for stationary singularly perturbed convection-diffusion problems and in [7,8] for system of singularly perturbed problems. This work provides a convergence analysis of numerical solution in moving mesh context.…”

Section: Introductionmentioning

confidence: 99%

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Upwind Based Parameter Uniform Convergence Analysis for Two Parametric Parabolic Convection Diffusion Problems by Moving Mesh Methods

Das

Mehrmann

2015

Proc Appl Math and Mech

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A parabolic two parametric convection-diffusion reaction problem is considered for the moving mesh error analysis. The continuous problem is discretized by the first order upwind scheme on a non uniform mesh. A curvature based error monitor function is proposed to generate the layer adapted mesh. It is proved that the numerical solution converges to the exact solution on the mesh obtained by the equidistribution of the proposed monitor function. The convergence is first order accurate. The present analysis generalizes the results obtained in earlier publications [8,9].

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“…The convergence is first order accurate. The present analysis generalizes the results obtained in earlier publications [8,9].…”

supporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Upwind Based Parameter Uniform Convergence Analysis for Two Parametric Parabolic Convection Diffusion Problems by Moving Mesh Methods

Das

Mehrmann

2015

Proc Appl Math and Mech

Self Cite

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“…For example, if epsilon in (1) is very small then adaptive mesh generations are necessary. Please refer to ( [2], [3], [4], [5], [6], [7]) for more detail on numerical methods which requires adaptive mesh generations with the error analysis on these meshes.…”

Section: Discussionmentioning

confidence: 99%

A Predator-prey Model with Predator Population Saturation

Hoff¹,

Fay²

2016

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In this article, a new predator-prey model having predator saturation is proposed. The model resembles a classical Rosenzweig-MacArthur type model, but comes with an added function, the population saturation function of the predator. This function of the predator population is a factor in the predator fertility term in the model. Consequently the model behaves better than the Rosenzweig-MacArthur model since all solutions are bounded within the population quadrant. An invariant region arises where the Poincaré-Bendixon theorem can be applied. In most cases there is but a single critical value, either an attracting spiral point suggesting a stable population pair or an unstable node, resulting in a unique limit cycle. This model is fully described and an analysis of the stability of critical values is provided. The robustness of the model is demonstrated based on the classification of Gunawardena [8].

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“…A moving mesh technique by the equidistribution of a positive monitor function is taken to generate meshes and it shows first order accuracy [21]. A system of coupled singularly perturbed 35 reaction-diffusion problems having diffusion parameters with different magnitudes is considered in [22]. Central difference scheme is used to discretize the problem on equidistribution mesh to obtain an optimal second-order parameter uniform convergence.…”

Section: Introductionmentioning

confidence: 99%

A parameter robust higher order numerical method for singularly perturbed two parameter problems with non-smooth data

Chandru

Prabha

Shanthi

2017

Journal of Computational and Applied Mathematics

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Please cite this article as: M. Chandru, T. Prabha, V. Shanthi, A parameter robust higher order numerical method for singularly perturbed two parameter problems with non-smooth data, Journal of Computational and Applied Mathematics (2016), http://dx. AbstractA singularly perturbed second order ordinary differential equation having two parameters with a discontinuous source term is presented for numerical analysis. Theoretical bounds on the derivatives, regular and singular components of the solution are derived. A hybrid monotone difference scheme with the method of averaging at the discontinuous point is constructed on Shishkin mesh. Parameter-uniform error bounds for the numerical approximation are established. Numerical results are presented which support the theoretical result.

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Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction–diffusion boundary-value problems

Cited by 51 publications

References 24 publications

Upwind Based Parameter Uniform Convergence Analysis for Two Parametric Parabolic Convection Diffusion Problems by Moving Mesh Methods

Upwind Based Parameter Uniform Convergence Analysis for Two Parametric Parabolic Convection Diffusion Problems by Moving Mesh Methods

A Predator-prey Model with Predator Population Saturation

A parameter robust higher order numerical method for singularly perturbed two parameter problems with non-smooth data

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