A numerical method for singular perturbation problems arising in chemical reactor theory

Jayakumar, J. S.; Ramanujam, N.

doi:10.1016/0898-1221(94)90078-7

Cited by 24 publications

(6 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we presented a numerical method to solve third-order SP-BVPs for ODEs subject to particular type of boundary conditions by adopting the techniques of [6,21,32,37] and [10]- [13], [36] who used to solve secondorder and third-order SPBVPs for ODEs. The boundary conditions help us to reduce the given third order ordinary differential equation into a weakly coupled system of one first order and one second order equation subject to initial and boundary conditions, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…Following the Boundary Value Technique (BVT) of Roberts [22], Vigo-Aguiar [37], Valarmathi [32] and using the basic idea underlying the method suggested in Khuri [40,41], Jayakumar [6] and Natesan [10,16] we in the present paper, suggest a new computational method which makes use of the zero order asymptotic expansion approximation, BVT and Shooting method to obtain a numerical solution for the derivative of SPBVPs for third order ODEs of reactiondiffusion type of the form:…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Reaction-Diffusion Type

Roja¹,

Tamilselvan²

2017

Journal of applied mathematics & informatics

View full text Add to dashboard Cite

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ε multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Reaction-Diffusion Type

Roja¹,

Tamilselvan²

2017

Journal of applied mathematics & informatics

View full text Add to dashboard Cite

show abstract

“…An extensive study and analysis have been carried on for more than two decades. A good amount of research works is reported on the qualitative and quantitative analysis for singularly perturbed of boundary value problems [1][2][3][4]. In this study, we consider Third order singularly perturbed convection-diffusion perturbedboundary value problem of the form:…”

Section: Introductionmentioning

confidence: 99%

On Computational Assessment of Perturbation Parameter (Ɛ) on Third Order Singularly Perturbed Convection-Diffusion Boundary Value Problems

Iyanda¹,

Iyadunni²

2019

JAMC

View full text Add to dashboard Cite

Two point boundary value problems for third order singularly perturbed ordinary differential equation in which the highest order derivative is multiplied by perturbation parameter ε was examined. Exponentially Fitted Collocation Approximate Method was proposed and employed to assess the effect of perturbation parameter (ɛ) on the highest derivation of the singularly perturbed convection-diffusion equation. The perturbation parameter (ɛ) was varied from 0.5 to 0.1 and obtained the corresponding solutions of y(x). The results demonstrate that this method is very convenient for solving boundary value problems and also can be successfully apply to a lot of practical engineering and physical problems.

show abstract

“…Also, for some numerical methods and their convergence analysis, one may refer: Farrell et al [4], Miller et al [5], Roos et al [6]. In the articles [7][8][9][10][11], many researcher have followed different numerical approach combining fitted mesh methods and fitted operator methods for solving SPPs where as [12] gives an erudite outline on the numerical methods for SPPs. In [13,14] efficient numerical methods are used for SPPs with an delay (or shift) term.…”

mentioning

confidence: 97%

An Efficient Numerical Method for Singularly Perturbed Two Point Boundary Value Problems Exhibiting Boundary Layers

Reddy¹,

Mohapatra

2015

Natl. Acad. Sci. Lett.

View full text Add to dashboard Cite

In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layers. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of algorithm is investigated. It is shown that proposed technique provides first order accuracy independent of perturbation parameter. Linear and nonlinear problems are solved by proposed method and numerical results are presented to illustrate the present technique.

show abstract

A numerical method for singular perturbation problems arising in chemical reactor theory

Cited by 24 publications

References 12 publications

Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Reaction-Diffusion Type

Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Reaction-Diffusion Type

On Computational Assessment of Perturbation Parameter (Ɛ) on Third Order Singularly Perturbed Convection-Diffusion Boundary Value Problems

An Efficient Numerical Method for Singularly Perturbed Two Point Boundary Value Problems Exhibiting Boundary Layers

Contact Info

Product

Resources

About