1982
DOI: 10.1007/bf01934448
|View full text |Cite
|
Sign up to set email alerts
|

Improving the accuracy of finite difference methods for solving boundary value ordinary differential equations

Abstract: Abstract.It is shown that by introducing one or three interpolated values in each subinterval the local truncation error of finite difference (box, gap and deferred correction) methods can be decreased by two to four orders of magnitude when solving two point boundary value ordinary differential equations.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1

Citation Types

0
3
0

Year Published

1983
1983
1986
1986

Publication Types

Select...
4
1

Relationship

1
4

Authors

Journals

citations
Cited by 5 publications
(3 citation statements)
references
References 8 publications
(7 reference statements)
0
3
0
Order By: Relevance
“…This problem leads to relatively less accurate results than the other problems [1,[5][6] due to the large values~of the derivatives of f. It is pointed out in [1] that for this problem the Trapezoidal Rule method required 21° mesh points for 10 -6 accuracy, and the deferred correction method needed 65 mesh points with 7 corrections. All of our computations were performed in double precision on a UNIVAC 1100 using FORTRAN (ASC II) Level 9R1.…”
Section: Computational Resultsmentioning
confidence: 93%
See 2 more Smart Citations
“…This problem leads to relatively less accurate results than the other problems [1,[5][6] due to the large values~of the derivatives of f. It is pointed out in [1] that for this problem the Trapezoidal Rule method required 21° mesh points for 10 -6 accuracy, and the deferred correction method needed 65 mesh points with 7 corrections. All of our computations were performed in double precision on a UNIVAC 1100 using FORTRAN (ASC II) Level 9R1.…”
Section: Computational Resultsmentioning
confidence: 93%
“…The last section contains the results of some numerical experiments on a difficult test problem. This paper makes use of some of our results given in a recent paper in this journal [5]. The values of f~-3/4, f~-1/2 and f~-1/4 are computed by the appropriate interpolation formulas given in [5], such that (2.1) and (2.2) are, respectively, O(h s) and O(h7).…”
Section: 1) Y'(x)-f (X Y(x)) =mentioning
confidence: 98%
See 1 more Smart Citation