Implicit Three-Point Block Numerical Algorithm for Solving Third Order Initial Value Problem Directly with Applications Article Swipe
Reem Allogmany
,
Fudziah Ismail
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.3390/math8101771
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.3390/math8101771
Recently, direct methods that involve higher derivatives to numerically approximate higher order initial value problems (IVPs) have been explored, which aim to construct numerical methods with higher order and very high precision of the solutions. This article aims to construct a fourth and fifth derivative, three-point implicit block method to tackle general third-order ordinary differential equations directly. As a consequence of the increase in order acquired via the implicit block method of higher derivatives, a significant improvement in efficiency has been observed. The new method is derived in a block mode to simultaneously evaluate the approximations at three points. The derivation of the new method can be easily implemented. We established the proposed method’s characteristics, including order, zero-stability, and convergence. Numerical experiments are used to confirm the superiority of the method. Applications to problems in physics and engineering are given to assess the significance of the method.
Related Topics
Concepts
Convergence (economics)
Block (permutation group theory)
Construct (python library)
Initial value problem
Ordinary differential equation
Stability (learning theory)
Algorithm
Applied mathematics
Mathematics
Numerical analysis
Order (exchange)
Third order
Order of accuracy
Point (geometry)
Explicit and implicit methods
Numerical stability
Computer science
Mathematical optimization
Differential equation
Mathematical analysis
Geometry
Differential algebraic equation
Economics
Theology
Programming language
Economic growth
Philosophy
Machine learning
Finance
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/math8101771
- https://www.mdpi.com/2227-7390/8/10/1771/pdf?version=1602666345
- OA Status
- gold
- Cited By
- 15
- References
- 35
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3093350573
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3093350573Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3390/math8101771Digital Object Identifier
- Title
-
Implicit Three-Point Block Numerical Algorithm for Solving Third Order Initial Value Problem Directly with ApplicationsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2020Year of publication
- Publication date
-
2020-10-14Full publication date if available
- Authors
-
Reem Allogmany, Fudziah IsmailList of authors in order
- Landing page
-
https://doi.org/10.3390/math8101771Publisher landing page
- PDF URL
-
https://www.mdpi.com/2227-7390/8/10/1771/pdf?version=1602666345Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://www.mdpi.com/2227-7390/8/10/1771/pdf?version=1602666345Direct OA link when available
- Concepts
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Convergence (economics), Block (permutation group theory), Construct (python library), Initial value problem, Ordinary differential equation, Stability (learning theory), Algorithm, Applied mathematics, Mathematics, Numerical analysis, Order (exchange), Third order, Order of accuracy, Point (geometry), Explicit and implicit methods, Numerical stability, Computer science, Mathematical optimization, Differential equation, Mathematical analysis, Geometry, Differential algebraic equation, Economics, Theology, Programming language, Economic growth, Philosophy, Machine learning, FinanceTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
15Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 3, 2024: 4, 2023: 3, 2022: 1, 2021: 4Per-year citation counts (last 5 years)
- References (count)
-
35Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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