Numerical solution of a convection diffusion problem with Robin boundary conditions

Ansari, Ali; Hegarty, Alan F.

doi:10.1016/s0377-0427(02)00913-5

Cited by 36 publications

(21 citation statements)

References 3 publications

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“…Lemma 1 [14,16] For each integer k satisfying 0 ≤ k ≤ 3, the solution w 1 of (8), (9) satisfies the bounds…”

Section: Theorem 4 For Each Integer K Satisfyingmentioning

confidence: 99%

“…Using a standard stability and consistency argument coupled with the obvious barrier func- [14], one can deduce that…”

Section: Error Analysismentioning

confidence: 99%

“…Let us first consider the magnitude of the truncation error at the point of discontinuity x = d. Using the procedure following in [3] and the derivative estimate established in [14] the following result can be obtain…”

Section: Error Analysismentioning

confidence: 99%

“…The nature of problem discussed in the Dirichlet case α 1 = 1, β 1 = 0, α 2 = 1 and β 2 = 0 and in the Neumann case α 1 = 0, β 1 = 1, α 2 = 0 and β 2 = 1 in [14]. For detailed study one may refer [14,15].…”

Section: Introductionmentioning

confidence: 99%

“…Various methods are available in literature to obtain numerical solution to singularly perturbed differential equation (1) subject to Robin boundary conditions when f is smooth on Ω [14,[16][17][18][19][20]. Some recent works have been done in similar type of problem with smooth data as follows.…”

Section: Introductionmentioning

confidence: 99%

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Fitted Mesh Method for Singularly Perturbed Robin Type Boundary Value Problem with Discontinuous Source Term

Chandru

Shanthi

2015

Int. J. Appl. Comput. Math

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In this paper, second order singularly perturbed convection-diffusion Robin type problem with a discontinuous source term is considered. Due to the discontinuity interior layers appears in the solution. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh for the boundary and interior layers. The method is shown to be parameter uniformly convergent with respect to the singular perturbation parameter. Numerical examples are presented to illustrate the theoretical results.

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“…Lemma 1 [14,16] For each integer k satisfying 0 ≤ k ≤ 3, the solution w 1 of (8), (9) satisfies the bounds…”

Section: Theorem 4 For Each Integer K Satisfyingmentioning

confidence: 99%

“…Using a standard stability and consistency argument coupled with the obvious barrier func- [14], one can deduce that…”

Section: Error Analysismentioning

confidence: 99%

Section: Error Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fitted Mesh Method for Singularly Perturbed Robin Type Boundary Value Problem with Discontinuous Source Term

Chandru

Shanthi

2015

Int. J. Appl. Comput. Math

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A parameter‐uniform scheme for singularly perturbed partial differential equations with a time lag

Kumar

Kumari

2019

Numerical Methods Partial

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A numerical scheme for a class of singularly perturbed delay parabolic partial differential equations which has wide applications in the various branches of science and engineering is suggested. The solution of these problems exhibits a parabolic boundary layer on the lateral side of the rectangular domain which continuously depends on the perturbation parameter. For the small perturbation parameter, the standard numerical schemes for the solution of these problems fail to resolve the boundary layer(s) and the oscillations occur near the boundary layer. Thus, in this paper to resolve the boundary layer the extended cubic B-spline basis functions consisting of a free parameter are used on a fitted-mesh. The extended B-splines are the extension of classical B-splines. To find the best value of the optimization technique is adopted. The extended cubic B-splines are an advantage over the classical B-splines as for some optimized value of the solution obtained by the extended B-splines is better than the solution obtained by classical B-splines. The method is shown to be first-order accurate in t and almost the second-order accurate in x. It is also shown that this method is better than some existing methods. Several test problems are encountered to validate the theoretical results. KEYWORDS delay partial differential equations, extended B-splines, free parameter, parabolic boundary layers, parameter-uniform convergence, piecewise-uniform mesh, singular perturbation, time delay Numer Methods Partial Differential Eq. 2020;36:868-886. wileyonlinelibrary.com/journal/num

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Robust Numerical Technique for a Class of Singularly Perturbed Nonlinear System of n-Differential Equations With Robin Boundary Conditions

Ishwariya

2024

Lecture Notes in Networks and Systems

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Numerical solution of a convection diffusion problem with Robin boundary conditions

Cited by 36 publications

References 3 publications

Fitted Mesh Method for Singularly Perturbed Robin Type Boundary Value Problem with Discontinuous Source Term

Fitted Mesh Method for Singularly Perturbed Robin Type Boundary Value Problem with Discontinuous Source Term

A parameter‐uniform scheme for singularly perturbed partial differential equations with a time lag

Robust Numerical Technique for a Class of Singularly Perturbed Nonlinear System of n-Differential Equations With Robin Boundary Conditions

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