Asymptotic error expansions for stiff equations: an analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case

1989 ◽  
Vol 56 (5) ◽  
pp. 469-499 ◽  
Author(s):  
W. Auzinger ◽  
R. Frank
Keyword(s):  
Stiff Equations ◽  
Asymptotic Error ◽  
Asymptotic Error Expansions

Asymptotic error expansions for stiff equations: Applications

Computing ◽  
1990 ◽  
Vol 43 (3) ◽  
pp. 223-253 ◽  
Author(s):  
W. Auzinger ◽  
R. Frank ◽  
G. Kirlinger
Keyword(s):  
Stiff Equations ◽  
Asymptotic Error ◽  
Asymptotic Error Expansions

Asymptotic Error Expansions for Spline Interpolation

1984 ◽  
Vol 27 (3) ◽  
pp. 337-344 ◽  
Author(s):  
H. P. Dikshit ◽  
A. Sharma ◽  
J. Tzimbalario
Keyword(s):  
Error Bounds ◽  
Finite Interval ◽  
Spline Interpolation ◽  
Asymptotic Error ◽  
End Conditions ◽  
Odd Degree ◽  
Error Expansion ◽  
Analysis Of Error ◽  
Asymptotic Error Expansions

AbstractDuring the last decade or so there has been a revival of interest in the analysis of error-bounds f(s)-S(s) for different classes of functions and their interpolatory splines of odd degree on a finite interval with variations on end conditions. Our object is to present a unified treatment of the asymptotic error expansion both for even and for odd degree interpolatory splines.

ON ASYMPTOTIC ERROR EXPANSIONS FOR SINGULAR BOUNDARY VALUE PROBLEMS

2001 ◽  
Vol 11 (01) ◽  
pp. 71-85 ◽  
Author(s):  
FLORIAN FROMMLET ◽  
EWA B. WEINMÜLLER
Keyword(s):  
Asymptotic Expansion ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Variational Equations ◽  
Asymptotic Error ◽  
Problem Data ◽  
Asymptotic Error Expansions

The existence of an asymptotic expansion for the global error of a standard three-point finite difference scheme applied to solve BVPs for ordinary differential equations of second order with a singularity of the first kind is considered. It turns out that even for very smooth problem data such asymptotic expansion does not exist, in general. More precisely, its length is restricted by unbounded inhomogeneities occurring in variational equations due to the singularity.

Some recent applications of asymptotic error expansions to finite-difference schemes

1971 ◽  
Vol 323 (1553) ◽  
pp. 167-177 ◽  
Keyword(s):  
Finite Difference ◽  
Approximate Solutions ◽  
Difference Schemes ◽  
Linear Multistep Methods ◽  
Finite Difference Schemes ◽  
The Finite Element Method ◽  
Technical Device ◽  
Asymptotic Error ◽  
The Subject ◽  
Asymptotic Error Expansions

In this paper we will present some results on asymptotic error expansions of the approximate solutions of differential equations by finite-difference schemes. We will present some quite well-known material, in an effort to make the presentation self-contained, as well as discuss recent work by Engquist on linear multistep methods for initial-value problems, by Kreiss on extrapolation procedures for elliptic finite-difference schemes, by Pereyra and co-workers on iterated deferred-correction methods for elliptic equations and by the author and Hald on the finite-element method. Practical aspects of the subject as well as the use of error expansions as a technical device in theoretical numerical analysis are discussed.

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