New solitary wave solitons, analysis and simulations of the FitzHugh–Nagumo Model.
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| Title: | New solitary wave solitons, analysis and simulations of the FitzHugh–Nagumo Model. |
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| Authors: | Maurya, Devraj1 (AUTHOR) devraj_m@ma.iitr.ac.in, Singh, Ajeet1 (AUTHOR) ajeet_s@ma.iitr.ac.in, Jiwari, Ram1 (AUTHOR) ram.jiwari@ma.iitr.ac.in |
| Source: | Mathematics & Computers in Simulation. Oct2026, Vol. 248, p384-403. 20p. |
| Subjects: | Solitons, Finite element method, Uniqueness (Mathematics), Computer simulation, Mathematical models, Lyapunov functions, Approximation error |
| Abstract: | In this work, we construct new solitons of the FitzHugh–Nagumo model using the tanh–coth and Kudryashov methods. After that we analyze and simulate the model by developing a finite element method with BDF1 scheme. For existence and uniqueness of weak solutions, we use the fixed point theorem and a Lyapunov functional to derive a priori bounds. Optimal error estimates in H 1 and L 2 norms are derived for the FEM-BDF1 scheme and the nonlinearity is handled using the mean value theorem. In the numerical tests, we demonstrate the theoretical convergence rates and also capture the spiral wave behavior of the solution. • New solitons of FHN model are obtained by the tanh–coth and Kudryashov methods. • The model is analyzed and simulated by a FEM with BDF1 scheme. • Existence and uniqueness of weak solutions as well as a priori bounds are derived. • Optimal error estimates in Ĥ1 and L̂2 norms are derived. • Numerical validation is done through the obtained solutions using FEM. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194124883 AccessLevel: 6 PubType: Periodical PubTypeId: serialPeriodical PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: New solitary wave solitons, analysis and simulations of the FitzHugh–Nagumo Model. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Maurya%2C+Devraj%22">Maurya, Devraj</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> devraj_m@ma.iitr.ac.in</i><br /><searchLink fieldCode="AR" term="%22Singh%2C+Ajeet%22">Singh, Ajeet</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ajeet_s@ma.iitr.ac.in</i><br /><searchLink fieldCode="AR" term="%22Jiwari%2C+Ram%22">Jiwari, Ram</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ram.jiwari@ma.iitr.ac.in</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Computers+in+Simulation%22">Mathematics & Computers in Simulation</searchLink>. Oct2026, Vol. 248, p384-403. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Solitons%22">Solitons</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Uniqueness+%28Mathematics%29%22">Uniqueness (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+functions%22">Lyapunov functions</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this work, we construct new solitons of the FitzHugh–Nagumo model using the tanh–coth and Kudryashov methods. After that we analyze and simulate the model by developing a finite element method with BDF1 scheme. For existence and uniqueness of weak solutions, we use the fixed point theorem and a Lyapunov functional to derive a priori bounds. Optimal error estimates in H 1 and L 2 norms are derived for the FEM-BDF1 scheme and the nonlinearity is handled using the mean value theorem. In the numerical tests, we demonstrate the theoretical convergence rates and also capture the spiral wave behavior of the solution. • New solitons of FHN model are obtained by the tanh–coth and Kudryashov methods. • The model is analyzed and simulated by a FEM with BDF1 scheme. • Existence and uniqueness of weak solutions as well as a priori bounds are derived. • Optimal error estimates in Ĥ1 and L̂2 norms are derived. • Numerical validation is done through the obtained solutions using FEM. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.matcom.2026.04.027 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 384 Subjects: – SubjectFull: Solitons Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Uniqueness (Mathematics) Type: general – SubjectFull: Computer simulation Type: general – SubjectFull: Mathematical models Type: general – SubjectFull: Lyapunov functions Type: general – SubjectFull: Approximation error Type: general Titles: – TitleFull: New solitary wave solitons, analysis and simulations of the FitzHugh–Nagumo Model. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Maurya, Devraj – PersonEntity: Name: NameFull: Singh, Ajeet – PersonEntity: Name: NameFull: Jiwari, Ram IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 03784754 Numbering: – Type: volume Value: 248 Titles: – TitleFull: Mathematics & Computers in Simulation Type: main |
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