Robust numerical scheme for singularly perturbed convection–diffusion parabolic initial–boundary-value problems on equidistributed grids

Gowrisankar, S.; Natesan, Srinivasan

doi:10.1016/j.cpc.2014.04.004

Cited by 37 publications

(30 citation statements)

References 14 publications

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“…al. [1] and on layer-adapted mesh obtain through equidistribution by Gowrisankar and Natesan [2]. Also in [3], the authors solved the singularly perturbed DPDEs of convection-diffusion type by the upwind finite difference scheme on the Shishkin mesh.…”

Section: Model Problemmentioning

confidence: 98%

Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh

Das

Natesan

2015

Applied Mathematics and Computation

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Section: Model Problemmentioning

confidence: 98%

Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh

Das

Natesan

2015

Applied Mathematics and Computation

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“…For work on convection diffusion problem for SPPDDEs one can refer to [2,3,4,6,7,11]. Aditya and Manju [6] analyzed the weighted difference approximations on piecewise uniform mesh for singularly perturbed delay differential convection diffusion problems and established that the proposed scheme is L h 2 stable.…”

Section: Introductionmentioning

confidence: 99%

Robust numerical schemes for singularly perturbed delay parabolic convection-diffusion problems with degenerate coefficient

Rai

Yadav

2020

International Journal of Computer Mathematics

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This article studies a dirichlet boundary value problem for singularly perturbed time delay convection diffusion equation with degenerate coefficient. A priori explicit bounds are established on the solution and its derivatives. For asymptotic analysis of the spatial derivatives the solution is decomposed into regular and singular parts. To approximate the solution a numerical method is considered which consists of backward Euler scheme for time discretization on uniform mesh and a combination of midpoint upwind and central difference scheme for the spatial discretization on modified Shishkin mesh. Stability analysis is carried out, numerical results are presented and comparison is done with upwind scheme on uniform mesh as well as upwind scheme on Shishkin mesh to demonstrate the effectiveness of the proposed method. The convergence obtained in practical satisfies the theoretical predictions. ). Problem (1.2)-(1.4) covers the multiple turning points for p > 1. The solution of the problem (1.2)-(1.4) exhibit a parabolic boundary layer of width O( √ ε) in the neighbourhood of the left boundary Γ l as all the characteristic curves of the reduced problem are parallel to the boundary Γ r . The existence of the unique solution of the Problem (1.2)-(1.4) is guaranteed under the assumption

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“…It is well-known [12] that the implicit Euler method ensures the stability of the solution of (2.5) and if we denote the local truncation error in the (n + 1)-st time-step at a point…”

Section: The Space-time Continuous Problemmentioning

confidence: 99%

mentioning

confidence: 99%

“…Parabolic singularly perturbed initial boundary problems which only involve a diffusion parameter were considered in [11,12,22,23], where several kind of numerical techniques were developed for uniform convergence. In [11,12] a curvature based and in [25], an arc-length based monitor function is suggested to generate the boundary layer-adapted meshes for parabolic problems. Numerical methods using two-step backward difference time discretization can be found in [7,8,9], see also [30] for a detailed survey on time dependent singularly perturbed problems and appropriate efficient numerical methods.…”

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confidence: 99%

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Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters

2015

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Robust numerical scheme for singularly perturbed convection–diffusion parabolic initial–boundary-value problems on equidistributed grids

Cited by 37 publications

References 14 publications

Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh

Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh

Robust numerical schemes for singularly perturbed delay parabolic convection-diffusion problems with degenerate coefficient

Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters

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