Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 10, 1980 - Issue 1
Submit an article Journal homepage
31
Views
36
CrossRef citations to date
0
Altmetric
Original Articles

Singular perturbations of difference methods for linear ordinary differential equations

Hans-Jurgen Reinhardt
,
G. C. Hsiao
,
L. R. Abrahamsson
,
H. B. Keller
&
O. Kreiss
Pages 53-70 | Received 13 Jul 1978, Published online: 02 May 2007

Citations (36)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (4)

Aditya Kaushik & Manju Sharma. (2016) An optimal asymptotic-numerical method for convection dominated systems having exponential boundary layers. Journal of Difference Equations and Applications 22:9, pages 1307-1324.
Read now
Manoj Kumar, P. Singh & Hradyesh Kumar Mishra. (2007) An Initial-Value Technique for Singularly Perturbed Boundary Value Problems via Cubic Spline. International Journal for Computational Methods in Engineering Science and Mechanics 8:6, pages 419-427.
Read now
Mohan. K. Kadalbajoo & A. Appaji Rao. (1998) Parallel discrete invariant embedding algorithm for singular pertubation problems. International Journal of Computer Mathematics 66:1-2, pages 149-161.
Read now
Hans-Jüirgen Reinhardt. (1979) On asymptotic expansions in nonlinear, singularly perturbed difference equations . Numerical Functional Analysis and Optimization 1:6, pages 565-587.
Read now

Articles from other publishers (32)

Chein-Shan Liu, Essam R. El-Zahar & Chih-Wen Chang. (2022) Higher-Order Asymptotic Numerical Solutions for Singularly Perturbed Problems with Variable Coefficients. Mathematics 10:15, pages 2791.
Crossref
Jugal Mohapatra. (2018) A Computational Method for Solving Singularly Perturbed Boundary Value Problem. National Academy Science Letters 41:2, pages 117-120.
Crossref
Ram Kishun Lodhi & Hradyesh Kumar Mishra. (2017) Quintic B-spline method for solving second order linear and nonlinear singularly perturbed two-point boundary value problems. Journal of Computational and Applied Mathematics 319, pages 170-187.
Crossref
Awoke Andargie & Yanala Narsimha Reddy. (2012) Two Initial Value Problems Approach for Solving Singular Perturbations Problems. American Journal of Computational Mathematics 02:03, pages 213-216.
Crossref
Mohan K. Kadalbajoo & Devendra Kumar. (2009) Initial value technique for singularly perturbed two point boundary value problems using an exponentially fitted finite difference scheme. Computers & Mathematics with Applications 57:7, pages 1147-1156.
Crossref
Manoj Kumar, Hradyesh Kumar Mishra & Peetam Singh. (2009) A boundary value approach for a class of linear singularly perturbed boundary value problems. Advances in Engineering Software 40:4, pages 298-304.
Crossref
Manoj Kumar, Hradyesh Kumar Mishra & P. Singh. (2008) Numerical treatment of singularly perturbed two point boundary value problems using initial-value method. Journal of Applied Mathematics and Computing 29:1-2, pages 229-246.
Crossref
Mohan K. Kadalbajoo & Devendra Kumar. (2008) A non-linear single step explicit scheme for non-linear two-point singularly perturbed boundary value problems via initial value technique. Applied Mathematics and Computation 202:2, pages 738-746.
Crossref
H.M. Habib & E.R. El-Zahar. (2008) Variable step size initial value algorithm for singular perturbation problems using locally exact integration. Applied Mathematics and Computation 200:1, pages 330-340.
Crossref
Awoke Andargie & Y.N. Reddy. (2007) Fitted fourth-order tridiagonal finite difference method for singular perturbation problems. Applied Mathematics and Computation 192:1, pages 90-100.
Crossref
Andargie Awoke & Y.N. Reddy. (2007) An exponentially fitted special second-order finite difference method for solving singular perturbation problems. Applied Mathematics and Computation 190:2, pages 1767-1782.
Crossref
Rajesh K. Bawa. (2005) Spline based computational technique for linear singularly perturbed boundary value problems. Applied Mathematics and Computation 167:1, pages 225-236.
Crossref
Y.N. Reddy & P. Pramod Chakravarthy. (2004) An initial-value approach for solving singularly perturbed two-point boundary value problems. Applied Mathematics and Computation 155:1, pages 95-110.
Crossref
Y.N Reddy & P Pramod Chakravarthy. (2004) An exponentially fitted finite difference method for singular perturbation problems. Applied Mathematics and Computation 154:1, pages 83-101.
Crossref
Y.N Reddy & P Pramod Chakravarthy. (2003) Method of reduction of order for solving singularly perturbed two-point boundary value problems. Applied Mathematics and Computation 136:1, pages 27-45.
Crossref
T. Valanarasu & N. Ramanujan. (2003) Asymptotic Initial-Value Method for Singularly-Perturbed Boundary-Value Problems for Second-Order Ordinary Differential Equations. Journal of Optimization Theory and Applications 116:1, pages 167-182.
Crossref
M. K. Kadalbajoo & R. K. Bawa. (1996) Variable-mesh difference scheme for singularly-perturbed boundary-value problems using splines. Journal of Optimization Theory and Applications 90:2, pages 405-416.
Crossref
Zhang Wei-jiang. (1992) Exponential dichotomies of nonlinear discrete systems and its application to numerical analysis and computation. Applied Mathematics and Mechanics 13:1, pages 91-99.
Crossref
Wu Chi-kuang. (1989) Asymptotic solution for singular perturbation problems of difference equation. Applied Mathematics and Mechanics 10:12, pages 1091-1097.
Crossref
Mohan K. Kadalbajoo & Y.N. Reddy. (1989) Asymptotic and numerical analysis of singular perturbation problems: A survey. Applied Mathematics and Computation 30:3, pages 223-259.
Crossref
Mohan K Kadalbajoo & Y.N Reddy. (1988) An approximate method for solving a class of singular perturbation problems. Journal of Mathematical Analysis and Applications 133:2, pages 306-323.
Crossref
M. K. Kadalbajoo & Y. N. Reddy. (1987) A nonasymptotic method for singular perturbation problems. Journal of Optimization Theory and Applications 55:1, pages 73-84.
Crossref
Mohan K. Kadalbajoo & Y.N. Reddy. (1987) Numerical treatment of singularly perturbed two point boundary value problems. Applied Mathematics and Computation 21:2, pages 93-110.
Crossref
Mohan K. Kadalbajoo & Y.N. Reddy. (1987) Numerical solution of singular perturbation problems via deviating arguments. Applied Mathematics and Computation 21:3, pages 221-232.
Crossref
Mohan K. Kadalbajoo & Y.N. Reddy. (1987) Approximate method for the numerical solution of singular perturbation problems. Applied Mathematics and Computation 21:3, pages 185-199.
Crossref
M. K. Kadalbajoo & Y. N. Reddy. (1987) Numerical solution of singular perturbation problems by a terminal boundary-value technique. Journal of Optimization Theory and Applications 52:2, pages 243-254.
Crossref
M. K. Kadalbajoo & Y. N. Reddy. (1986) Numerical integration of a class of singular perturbation problems. Journal of Optimization Theory and Applications 51:3, pages 441-452.
Crossref
Mohan K. Kadalbajoo & Y.N. Reddy. (1986) The method of inner boundary condition: A new approach for solving singular perturbation problems. Journal of Computational Physics 62:2, pages 349-360.
Crossref
D.S. Naidu & A.K. Rao. (1985) Application of the singular perturbation method to a steam power system. Electric Power Systems Research 8:3, pages 219-226.
Crossref
V.R. Saksena, J. O'Reilly & P.V. Kokotovic. (1984) Singular perturbations and time-scale methods in control theory: Survey 1976–1983. Automatica 20:3, pages 273-293.
Crossref
H.-J. Reinhardt. 1984. Defect Correction Methods. Defect Correction Methods 43 66 .
D. S. Naidu & A. K. Rao. (2006) Singular perturbation analysis of the closed‐loop discrete optimal control problem. Optimal Control Applications and Methods 5:1, pages 19-37.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.