Formulation of a New Implicit Method for Group Implicit BBDF in Solving Related Stiff Ordinary Differential Equations Article Swipe
Norshakila Abd Rasid
,
Zarina Bibi İbrahim
,
Zanariah Abdul Majid
,
Fudziah Ismail
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.13189/ms.2021.090208
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.13189/ms.2021.090208
This paper proposed a new alternative approach of the implicit diagonal block backward differentiation formula (BBDF) to solve linear and nonlinear first-order stiff ordinary differential equations (ODEs). We generate the solver by manipulating the numbers of back values to achieve a higher-order possible using the interpolation procedure. The algorithm is developed and implemented in C ++ medium. The numerical integrator approximates few solution points concurrently with off-step points in a block scheme over a non-overlapping solution interval at a single iteration. The lower triangular matrix form of the implicit diagonal causes fewer differentiation coefficients and ultimately reduces the execution time during running codes. We choose two intermediate points as off-step points appropriately, which are proven to guarantee the method's zero stability. The off-step points help to increase the accuracy by optimizing the local truncation error. The proposed solver satisfied theoretical consistency and zero-stable requirements, leading to a convergent multistep method with third algebraic order. We used the well-known and standard linear and nonlinear stiff IVP problems used in literature for validation to measure the algorithm's accuracy and processor time efficiency. The performance metrics are validated by comparing them with a proven solver, and the output shows that the alternative method is better than the existing one.
Related Topics
Concepts
Mathematics
Explicit and implicit methods
Group (periodic table)
Ordinary differential equation
Numerical methods for ordinary differential equations
Applied mathematics
Backward differentiation formula
Mathematical analysis
Differential equation
Differential algebraic equation
Organic chemistry
Chemistry
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.13189/ms.2021.090208
- http://www.hrpub.org/download/20210330/MS8-13490610.pdf
- OA Status
- diamond
- Cited By
- 4
- References
- 15
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3164068100
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3164068100Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.13189/ms.2021.090208Digital Object Identifier
- Title
-
Formulation of a New Implicit Method for Group Implicit BBDF in Solving Related Stiff Ordinary Differential EquationsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-03-01Full publication date if available
- Authors
-
Norshakila Abd Rasid, Zarina Bibi İbrahim, Zanariah Abdul Majid, Fudziah IsmailList of authors in order
- Landing page
-
https://doi.org/10.13189/ms.2021.090208Publisher landing page
- PDF URL
-
https://www.hrpub.org/download/20210330/MS8-13490610.pdfDirect link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
diamondOpen access status per OpenAlex
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https://www.hrpub.org/download/20210330/MS8-13490610.pdfDirect OA link when available
- Concepts
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Mathematics, Explicit and implicit methods, Group (periodic table), Ordinary differential equation, Numerical methods for ordinary differential equations, Applied mathematics, Backward differentiation formula, Mathematical analysis, Differential equation, Differential algebraic equation, Organic chemistry, ChemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
4Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2022: 2, 2021: 1Per-year citation counts (last 5 years)
- References (count)
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15Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.of | 7, 35, 86 |
| abstract_inverted_index.to | 16, 38, 115, 125, 145, 171 |
| abstract_inverted_index.IVP | 164 |
| abstract_inverted_index.The | 47, 57, 81, 121, 135, 180 |
| abstract_inverted_index.and | 19, 51, 94, 141, 158, 161, 176, 192 |
| abstract_inverted_index.are | 113, 183 |
| abstract_inverted_index.few | 61 |
| abstract_inverted_index.for | 169 |
| abstract_inverted_index.new | 4 |
| abstract_inverted_index.the | 8, 29, 33, 44, 87, 97, 117, 127, 131, 156, 173, 193, 197, 203 |
| abstract_inverted_index.two | 105 |
| abstract_inverted_index.This | 0 |
| abstract_inverted_index.back | 36 |
| abstract_inverted_index.form | 85 |
| abstract_inverted_index.help | 124 |
| abstract_inverted_index.one. | 205 |
| abstract_inverted_index.over | 72 |
| abstract_inverted_index.than | 202 |
| abstract_inverted_index.that | 196 |
| abstract_inverted_index.them | 187 |
| abstract_inverted_index.time | 99, 178 |
| abstract_inverted_index.used | 155, 166 |
| abstract_inverted_index.with | 65, 150, 188 |
| abstract_inverted_index.zero | 119 |
| abstract_inverted_index.block | 11, 70 |
| abstract_inverted_index.fewer | 91 |
| abstract_inverted_index.local | 132 |
| abstract_inverted_index.lower | 82 |
| abstract_inverted_index.paper | 1 |
| abstract_inverted_index.shows | 195 |
| abstract_inverted_index.solve | 17 |
| abstract_inverted_index.stiff | 22, 163 |
| abstract_inverted_index.third | 151 |
| abstract_inverted_index.using | 43 |
| abstract_inverted_index.which | 112 |
| abstract_inverted_index.(BBDF) | 15 |
| abstract_inverted_index.better | 201 |
| abstract_inverted_index.causes | 90 |
| abstract_inverted_index.choose | 104 |
| abstract_inverted_index.codes. | 102 |
| abstract_inverted_index.during | 100 |
| abstract_inverted_index.error. | 134 |
| abstract_inverted_index.linear | 18, 160 |
| abstract_inverted_index.matrix | 84 |
| abstract_inverted_index.method | 149, 199 |
| abstract_inverted_index.order. | 153 |
| abstract_inverted_index.output | 194 |
| abstract_inverted_index.points | 63, 67, 107, 110, 123 |
| abstract_inverted_index.proven | 114, 190 |
| abstract_inverted_index.scheme | 71 |
| abstract_inverted_index.single | 79 |
| abstract_inverted_index.solver | 30, 137 |
| abstract_inverted_index.values | 37 |
| abstract_inverted_index.(ODEs). | 26 |
| abstract_inverted_index.achieve | 39 |
| abstract_inverted_index.formula | 14 |
| abstract_inverted_index.leading | 144 |
| abstract_inverted_index.measure | 172 |
| abstract_inverted_index.medium. | 56 |
| abstract_inverted_index.metrics | 182 |
| abstract_inverted_index.numbers | 34 |
| abstract_inverted_index.reduces | 96 |
| abstract_inverted_index.running | 101 |
| abstract_inverted_index.solver, | 191 |
| abstract_inverted_index.accuracy | 128, 175 |
| abstract_inverted_index.approach | 6 |
| abstract_inverted_index.backward | 12 |
| abstract_inverted_index.diagonal | 10, 89 |
| abstract_inverted_index.existing | 204 |
| abstract_inverted_index.generate | 28 |
| abstract_inverted_index.implicit | 9, 88 |
| abstract_inverted_index.increase | 126 |
| abstract_inverted_index.interval | 76 |
| abstract_inverted_index.method's | 118 |
| abstract_inverted_index.off-step | 66, 109, 122 |
| abstract_inverted_index.ordinary | 23 |
| abstract_inverted_index.possible | 42 |
| abstract_inverted_index.problems | 165 |
| abstract_inverted_index.proposed | 2, 136 |
| abstract_inverted_index.solution | 62, 75 |
| abstract_inverted_index.standard | 159 |
| abstract_inverted_index.algebraic | 152 |
| abstract_inverted_index.algorithm | 48 |
| abstract_inverted_index.comparing | 186 |
| abstract_inverted_index.developed | 50 |
| abstract_inverted_index.equations | 25 |
| abstract_inverted_index.execution | 98 |
| abstract_inverted_index.guarantee | 116 |
| abstract_inverted_index.multistep | 148 |
| abstract_inverted_index.nonlinear | 20, 162 |
| abstract_inverted_index.numerical | 58 |
| abstract_inverted_index.processor | 177 |
| abstract_inverted_index.satisfied | 138 |
| abstract_inverted_index.validated | 184 |
| abstract_inverted_index.convergent | 147 |
| abstract_inverted_index.integrator | 59 |
| abstract_inverted_index.iteration. | 80 |
| abstract_inverted_index.literature | 168 |
| abstract_inverted_index.optimizing | 130 |
| abstract_inverted_index.procedure. | 46 |
| abstract_inverted_index.stability. | 120 |
| abstract_inverted_index.triangular | 83 |
| abstract_inverted_index.truncation | 133 |
| abstract_inverted_index.ultimately | 95 |
| abstract_inverted_index.validation | 170 |
| abstract_inverted_index.well-known | 157 |
| abstract_inverted_index.algorithm's | 174 |
| abstract_inverted_index.alternative | 5, 198 |
| abstract_inverted_index.consistency | 140 |
| abstract_inverted_index.efficiency. | 179 |
| abstract_inverted_index.first-order | 21 |
| abstract_inverted_index.implemented | 52 |
| abstract_inverted_index.performance | 181 |
| abstract_inverted_index.theoretical | 139 |
| abstract_inverted_index.zero-stable | 142 |
| abstract_inverted_index.approximates | 60 |
| abstract_inverted_index.coefficients | 93 |
| abstract_inverted_index.concurrently | 64 |
| abstract_inverted_index.differential | 24 |
| abstract_inverted_index.higher-order | 41 |
| abstract_inverted_index.intermediate | 106 |
| abstract_inverted_index.manipulating | 32 |
| abstract_inverted_index.interpolation | 45 |
| abstract_inverted_index.requirements, | 143 |
| abstract_inverted_index.appropriately, | 111 |
| abstract_inverted_index.differentiation | 13, 92 |
| abstract_inverted_index.non-overlapping | 74 |
| cited_by_percentile_year.max | 96 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile.value | 0.720836 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |