An improved differential transform scheme implementation on the generalized Allen–Cahn equation governing oil pollution dynamics in oceanography
Studies in computational mathematics have taken a fantastic aesthetics in interdisciplinary fields as researchers in this area have resiliently adopted constructive methods, schemes, algorithms, and techniques on the nonlinear differential equations, to succinctly analyze the dynamical behavior of e...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-12-01
|
| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818122000808 |
| _version_ | 1811201532495921152 |
|---|---|
| author | Timilehin Kingsley Akinfe Adedapo Chris Loyinmi |
| author_facet | Timilehin Kingsley Akinfe Adedapo Chris Loyinmi |
| author_sort | Timilehin Kingsley Akinfe |
| collection | DOAJ |
| description | Studies in computational mathematics have taken a fantastic aesthetics in interdisciplinary fields as researchers in this area have resiliently adopted constructive methods, schemes, algorithms, and techniques on the nonlinear differential equations, to succinctly analyze the dynamical behavior of established models for which this study has yet, coupled the Elzaki integral transform as a before treatment to complement domain decomposition for increased accuracy and convergence with the projected differential transform method, yielding an improved differential transform technique (EPDTM), on a cogent extract of the generalized oil pollution and spillage’s governing equation viz: the Allen–Cahn equation which describes oil pollution dynamics, reaction–diffusion mechanisms, and mechanics of crystalline solids with an interfacial thickness parameter ɛ, with applications in solid-state physics, imaging, plasma physics, material science and so on, for which material and plasma sciences may benefit from these solutions. The validatory analysis of this hybrid technique via tables, graphical illustrations with arbitrarily varied parameters, and convergence analysis ascertained the consistency, uniqueness, and convergence of our obtained analytical results, thus, distinct from existing works of the literature.Notably, the dynamical scrutiny carried out utilizing the developed EPDTM solution revealed an increase in the model’s periodicity with a constant wavelength for each increase in the interfacial thickness parameter ɛ, which is realistically valid for the Allen–Cahn model. |
| first_indexed | 2024-04-12T02:22:04Z |
| format | Article |
| id | doaj.art-3b3cc70e0ff4426584fd1855a1f238df |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-04-12T02:22:04Z |
| publishDate | 2022-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-3b3cc70e0ff4426584fd1855a1f238df2022-12-22T03:52:05ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812022-12-016100416An improved differential transform scheme implementation on the generalized Allen–Cahn equation governing oil pollution dynamics in oceanographyTimilehin Kingsley Akinfe0Adedapo Chris Loyinmi1Department of Mathematics, University of Lagos, Akoka, Lagos State, Nigeria; Department of Mathematics, Tai Solarin University of Education, Ijagun, Ijebu ode, Ogun state, Nigeria; Corresponding author at: Department of Mathematics, Tai Solarin University of Education, Ijagun, Ijebu ode, Ogun state, Nigeria.Department of Mathematics, Tai Solarin University of Education, Ijagun, Ijebu ode, Ogun state, NigeriaStudies in computational mathematics have taken a fantastic aesthetics in interdisciplinary fields as researchers in this area have resiliently adopted constructive methods, schemes, algorithms, and techniques on the nonlinear differential equations, to succinctly analyze the dynamical behavior of established models for which this study has yet, coupled the Elzaki integral transform as a before treatment to complement domain decomposition for increased accuracy and convergence with the projected differential transform method, yielding an improved differential transform technique (EPDTM), on a cogent extract of the generalized oil pollution and spillage’s governing equation viz: the Allen–Cahn equation which describes oil pollution dynamics, reaction–diffusion mechanisms, and mechanics of crystalline solids with an interfacial thickness parameter ɛ, with applications in solid-state physics, imaging, plasma physics, material science and so on, for which material and plasma sciences may benefit from these solutions. The validatory analysis of this hybrid technique via tables, graphical illustrations with arbitrarily varied parameters, and convergence analysis ascertained the consistency, uniqueness, and convergence of our obtained analytical results, thus, distinct from existing works of the literature.Notably, the dynamical scrutiny carried out utilizing the developed EPDTM solution revealed an increase in the model’s periodicity with a constant wavelength for each increase in the interfacial thickness parameter ɛ, which is realistically valid for the Allen–Cahn model.http://www.sciencedirect.com/science/article/pii/S2666818122000808Oil pollution dynamicsReaction–diffusion equationComputational materials scienceElzaki integral transformHybrid methodDomain decomposition |
| spellingShingle | Timilehin Kingsley Akinfe Adedapo Chris Loyinmi An improved differential transform scheme implementation on the generalized Allen–Cahn equation governing oil pollution dynamics in oceanography Partial Differential Equations in Applied Mathematics Oil pollution dynamics Reaction–diffusion equation Computational materials science Elzaki integral transform Hybrid method Domain decomposition |
| title | An improved differential transform scheme implementation on the generalized Allen–Cahn equation governing oil pollution dynamics in oceanography |
| title_full | An improved differential transform scheme implementation on the generalized Allen–Cahn equation governing oil pollution dynamics in oceanography |
| title_fullStr | An improved differential transform scheme implementation on the generalized Allen–Cahn equation governing oil pollution dynamics in oceanography |
| title_full_unstemmed | An improved differential transform scheme implementation on the generalized Allen–Cahn equation governing oil pollution dynamics in oceanography |
| title_short | An improved differential transform scheme implementation on the generalized Allen–Cahn equation governing oil pollution dynamics in oceanography |
| title_sort | improved differential transform scheme implementation on the generalized allen cahn equation governing oil pollution dynamics in oceanography |
| topic | Oil pollution dynamics Reaction–diffusion equation Computational materials science Elzaki integral transform Hybrid method Domain decomposition |
| url | http://www.sciencedirect.com/science/article/pii/S2666818122000808 |
| work_keys_str_mv | AT timilehinkingsleyakinfe animproveddifferentialtransformschemeimplementationonthegeneralizedallencahnequationgoverningoilpollutiondynamicsinoceanography AT adedapochrisloyinmi animproveddifferentialtransformschemeimplementationonthegeneralizedallencahnequationgoverningoilpollutiondynamicsinoceanography AT timilehinkingsleyakinfe improveddifferentialtransformschemeimplementationonthegeneralizedallencahnequationgoverningoilpollutiondynamicsinoceanography AT adedapochrisloyinmi improveddifferentialtransformschemeimplementationonthegeneralizedallencahnequationgoverningoilpollutiondynamicsinoceanography |