Discontinuous Galerkin solution of the convection-diffusion-reaction equations in fluidized beds

Varma, V. Dhanya; Chamakuri, Nagaiah; Nadupuri, Suresh Kumar

doi:10.1016/j.apnum.2020.02.008

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…In this paper, we consider a new governing problem having both small delay on the convection term and large delay. Additionally, in recent years the in-depth correlative physical analysis of the problem under consideration have been done by the authors [10]- [18]. As far as the researchers' knowledge numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.…”

Section: Introductionmentioning

confidence: 99%

Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay

Debela,

Duressa

2023

Acta Universitatis Sapientiae, Mathematica

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In this paper, singularly perturbed differential equations having both small and large delay are considered. The considered problem contains large delay parameter on the reaction term and small delay parameter on the convection term. The solution of the problem exhibits interior layer due to the delay parameter and strong right boundary layer due to the small perturbation parameter ε. The resulting singularly perturbed problem is solved using exponential fitted operator method. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, one model problem is considered for numerical experimentation.

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Section: Introductionmentioning

confidence: 99%

Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay

Debela,

Duressa

2023

Acta Universitatis Sapientiae, Mathematica

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show abstract

“…In this paper, we consider a new governing problem having both small delay on convection term and large delay. Additionally, in recent years the correlative physical phenomena in-depth of the problem under consideration have been done by the authors [13][14][15][16][17]. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.…”

Section: Introductionmentioning

confidence: 99%

Robust numerical method for singularly perturbed differential equations having both large and small delay

Debela

2021

AJMS

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PurposeThe purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay.Design/methodology/approachThis study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay. The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation.FindingsThe stability of the developed numerical method is established and its uniform convergence is proved. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values of the perturbation parameter and mesh points.Originality/valueIn this paper, the authors consider a new governing problem having both small delay on convection term and large delay. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.

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A posteriori error estimates and an adaptive finite element solution for the system of unsteady convection-diffusion-reaction equations in fluidized beds

Varma

Nadupuri

Chamakuri

2021

Applied Numerical Mathematics

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Discontinuous Galerkin solution of the convection-diffusion-reaction equations in fluidized beds

Cited by 3 publications

References 17 publications

Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay

Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay

Robust numerical method for singularly perturbed differential equations having both large and small delay

A posteriori error estimates and an adaptive finite element solution for the system of unsteady convection-diffusion-reaction equations in fluidized beds

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