Trigonometrically-Fitted Fifth Order Four-Step Predictor-Corrector Method for Solving Linear Ordinary Differential Equations with Oscillatory Solutions Article Swipe
Mohammed Salih
,
Fudziah Ismail
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.47836/mjms.16.4.07
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.47836/mjms.16.4.07
In this paper, we proposed a trigonometrically-fitted fifth order four-step predictor-corrector method based on the four-step Adams-Bashforth method as predictor and five-step Adams-Moulton method as corrector to solve linear ordinary differential equations with oscillatory solutions. This method is constructed which exactly integrate initial value problems whose solutions can be expressed as linear combinations of the set functions {sin(υx),cos(υx)} with υ ∈ R, where v represents an approximation of the frequency of the problem. The frequency will be used in the method to raise the accuracy of the solution. Stability of the proposed method is examined and the corresponding region of stability is depicted. The new fifth algebraic order trigonometrically-fitted predictor-corrector method is applied to solve the initial value problems whose solutions involved trigonometric functions. Numerical results presented proved that the prospective method is more efficient than the widely used methods for the numerical solution of linear ordinary differential equations with oscillating solutions.
Related Topics
Concepts
Mathematics
Predictor–corrector method
Ordinary differential equation
Linear multistep method
Trigonometry
Stability (learning theory)
Set (abstract data type)
Mathematical analysis
Applied mathematics
Initial value problem
Linear differential equation
Trigonometric functions
Differential equation
Algebraic number
Backward differentiation formula
Differential algebraic equation
Computer science
Geometry
Programming language
Machine learning
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.47836/mjms.16.4.07
- https://mjms.upm.edu.my/fullpaper/2022-December-16-4/Salih, M. M.-739-748.pdf
- OA Status
- bronze
- Cited By
- 6
- References
- 22
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4312200155
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4312200155Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.47836/mjms.16.4.07Digital Object Identifier
- Title
-
Trigonometrically-Fitted Fifth Order Four-Step Predictor-Corrector Method for Solving Linear Ordinary Differential Equations with Oscillatory SolutionsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-12-23Full publication date if available
- Authors
-
Mohammed Salih, Fudziah IsmailList of authors in order
- Landing page
-
https://doi.org/10.47836/mjms.16.4.07Publisher landing page
- PDF URL
-
https://mjms.upm.edu.my/fullpaper/2022-December-16-4/Salih, M. M.-739-748.pdfDirect link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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bronzeOpen access status per OpenAlex
- OA URL
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https://mjms.upm.edu.my/fullpaper/2022-December-16-4/Salih, M. M.-739-748.pdfDirect OA link when available
- Concepts
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Mathematics, Predictor–corrector method, Ordinary differential equation, Linear multistep method, Trigonometry, Stability (learning theory), Set (abstract data type), Mathematical analysis, Applied mathematics, Initial value problem, Linear differential equation, Trigonometric functions, Differential equation, Algebraic number, Backward differentiation formula, Differential algebraic equation, Computer science, Geometry, Programming language, Machine learningTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
6Total citation count in OpenAlex
- Citations by year (recent)
-
2024: 4, 2023: 2Per-year citation counts (last 5 years)
- References (count)
-
22Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| corresponding_author_ids | https://openalex.org/A5061267070 |
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| institutions_distinct_count | 2 |
| corresponding_institution_ids | https://openalex.org/I12150220, https://openalex.org/I130343225 |
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| citation_normalized_percentile.is_in_top_10_percent | False |