Numerical Solution of Linear and Higher-order Delay Differential Equations using the Coded Differential Transform Method Article Swipe
Giriraj Methi
,
Ashish Kumar
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.20537/2076-7633-2019-11-6-1091-1099
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.20537/2076-7633-2019-11-6-1091-1099
The aim of the paper is to obtain a numerical solution for linear and higher-order delay differential equations (DDEs) using the coded differential transform method (CDTM). The CDTM is developed and applied to delay problems to show the efficiency of the proposed method. The coded differential transform method is a combination of the differential transform method and Mathematica software. We construct recursive relations for a few delay problems, which results in simultaneous equations, and solve them to obtain various series solution terms using the coded differential transform method. The numerical solution obtained by CDTM is compared with an exact solution. Numerical results and error analysis are presented for delay differential equations to show that the proposed method is suitable for solving delay differential equations. It is established that the delay differential equations under discussion are solvable in a specific domain. The error between the CDTM solution and the exact solution becomes very small if more terms are included in the series solution. The coded differential transform method reduces complex calculations, avoids discretization, linearization, and saves calculation time. In addition, it is easy to implement and robust. Error analysis shows that CDTM is consistent and converges fast. We obtain more accurate results using the coded differential transform method as compared to other methods.
Related Topics
Concepts
Delay differential equation
Mathematics
Numerical partial differential equations
Discretization
Differential equation
Examples of differential equations
Mathematical analysis
Applied mathematics
Differential algebraic equation
Ordinary differential equation
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.20537/2076-7633-2019-11-6-1091-1099
- http://crm.ics.org.ru/uploads/crmissues/crm_2019_6/19_Methi.pdf
- OA Status
- diamond
- Cited By
- 1
- References
- 6
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- 10
- OpenAlex ID
- https://openalex.org/W2997591782
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W2997591782Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.20537/2076-7633-2019-11-6-1091-1099Digital Object Identifier
- Title
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Numerical Solution of Linear and Higher-order Delay Differential Equations using the Coded Differential Transform MethodWork title
- Type
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articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2019Year of publication
- Publication date
-
2019-12-01Full publication date if available
- Authors
-
Giriraj Methi, Ashish KumarList of authors in order
- Landing page
-
https://doi.org/10.20537/2076-7633-2019-11-6-1091-1099Publisher landing page
- PDF URL
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https://crm.ics.org.ru/uploads/crmissues/crm_2019_6/19_Methi.pdfDirect link to full text PDF
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YesWhether a free full text is available
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diamondOpen access status per OpenAlex
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https://crm.ics.org.ru/uploads/crmissues/crm_2019_6/19_Methi.pdfDirect OA link when available
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Delay differential equation, Mathematics, Numerical partial differential equations, Discretization, Differential equation, Examples of differential equations, Mathematical analysis, Applied mathematics, Differential algebraic equation, Ordinary differential equationTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
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2023: 1Per-year citation counts (last 5 years)
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6Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.22899066 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |