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

被引：13

作者：

Reddy, N. Raji ^{[1
]}

Mohapatra, Jugal ^{[2
]}

机构：

[1] Jyothishmathi Inst Technol & Sci, Dept Math, Karimnagar 505481, India

[2] Natl Inst Technol Rourkela, Dept Math, Rourkela 769008, India

来源：

NATIONAL ACADEMY SCIENCE LETTERS-INDIA | 2015年 / 38卷 / 04期

关键词：

Singular perturbation problems; Thomas algorithm; Exponential fitting factor; Uniform convergence; FINITE-DIFFERENCE METHOD;

D O I：

10.1007/s40009-015-0350-z

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：355 / 359

页数：5

共 50 条

[1] An Efficient Numerical Method for Singularly Perturbed Two Point Boundary Value Problems Exhibiting Boundary Layers
N. Raji Reddy
Jugal Mohapatra
[J]. National Academy Science Letters, 2015, 38 : 355 - 359
[2] Numerical treatment of singularly perturbed two point boundary value problems exhibiting boundary layers
Attili, Basem S.
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (09) : 3504 - 3511
[3] Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers
Natesan, S
Jayakumar, J
Vigo-Aguiar, J
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 158 (01) : 121 - 134
[4] Numerical integration method for general singularly perturbed two point boundary value problems
Reddy, YN
Reddy, KA
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2002, 133 (2-3) : 351 - 373
[5] Parameter uniform numerical method for fourth order singularly perturbed turning point problems exhibiting boundary layers
Geetha, N.
Tamilselvan, A.
[J]. AIN SHAMS ENGINEERING JOURNAL, 2018, 9 (04) : 845 - 853
[6] Parameter Uniform Numerical Method for Third Order Singularly Perturbed Turning Point Problems Exhibiting Boundary Layers
Geetha N.
Tamilselvan A.
Subburayan V.
[J]. International Journal of Applied and Computational Mathematics, 2016, 2 (3) : 349 - 364
[7] Fitted mesh numerical method for singularly perturbed delay differential turning point problems exhibiting boundary layers
Rai, Pratima
Sharma, Kapil K.
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2012, 89 (07) : 944 - 961
[8] A Higher Order Accurate Numerical Method for Singularly Perturbed Two Point Boundary Value Problems
Kaushik A.
Kumar V.
Vashishth A.K.
[J]. Differential Equations and Dynamical Systems, 2017, 25 (2) : 267 - 285
[9] A computational method for solving singularly perturbed turning point problems exhibiting twin boundary layers
Natesan, S
Ramanujam, N
[J]. APPLIED MATHEMATICS AND COMPUTATION, 1998, 93 (2-3) : 259 - 275
[10] Numerical solution of singularly perturbed boundary value problems with power and logarithmic boundary layers
Andreev, VB
[J]. ANALYTICAL AND NUMERICAL METHODS FOR CONVECTION-DOMINATED AND SINGULARLY PERTURBED PROBLEMS, 2000, : 1 - 5

← 1 2 3 4 5 →