The DOI matches its Crossref record.
Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations
Abstract
A new iterative method has been developed for solving the large sets of algebraic equations that arise in the approximate solution of multidimensional partial differential equations by implicit numerical techniques. This method has several advantages over those now in use. First, its rate of convergence does not depend strongly on the nature of the coefficient matrix of the equations to be solved. Second, it is not sensitive to the choice of iteration parameters, and as a result, suitable parameters can be estimated from the coefficient matrix. Finally, it reduces significantly the computational effort needed to solve a set of equations. For a typical set of 961 equations, it was found to reduce the number of calculations by a factor of three, when compared to the most competitive of the older methods. It is expected that this advantage will be even greater for larger sets of equations.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Kirkpatrick, S. (1973) · Reviews of Modern Physics · doi:10.1103/revmodphys.45.574 · Cited by 5,260
ENHANCEMENTS OF THE SIMPLE METHOD FOR PREDICTING INCOMPRESSIBLE FLUID FLOWS
Van Doormaal, J. P., & Raithby, G. D. (1984) · Numerical Heat Transfer · doi:10.1080/01495728408961817 · Cited by 3,437
Bethke, C. M. (1985) · Journal of Geophysical Research: Solid Earth · doi:10.1029/jb090ib08p06817 · Cited by 445
Metadata
- Authors
- Stone, H. L.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1968-09
- Volume
- 5
- Issue
- 3
- Pages
- 530-558
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W2045244586
- Cited by
- 1,692
- References
- 0
- FWCI
- 4.01
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations. https://app.cochat.ai/papers/10.1137/0705044
- The paper
- Stone, H. L. (1968). Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations. SIAM Journal on Numerical Analysis. https://doi.org/10.1137/0705044
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
