Numerical investigation of the population distribution in heterogenous domain

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dc.contributor.advisorSadosvki, Alexey
dc.contributor.advisorVasilyeva, Maria
dc.contributor.authorHenry, Stephen Andre
dc.contributor.committeeMemberDenny, Diane
dc.contributor.committeeMemberMuddamallappa, Mallikarjunaiah
dc.date.accessioned2024-01-05T22:48:38Z
dc.date.available2024-01-05T22:48:38Z
dc.date.issued2023-08
dc.descriptionA thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mathematicsen_US
dc.description.abstractWe consider the spatial-temporal model of multi-species population distribution in two-dimensional heterogeneous domains. A coupled system of time-dependent diffusion-reaction equations describes the mathematical model of such problems. To solve the problem numerically, we construct an unstructured grid that resolves inclusions on the grid level and produces a semi-discrete system using a finite element method. For time approximation, we apply an explicit-implicit scheme where the reaction term of the equation is taken from the previous time layer. We present numerical results for several test problems to investigate the influence of the geometry and parameters on time to reach equilibrium and the final equilibrium state. An extension of the model is also considered, where we add a memory effect by introducing a time-fractional multi-species model. We derive an implicit finite difference approximation for time discretization based on Caputo’s time fractional derivative. A numerical investigation is performed for various orders of the time derivative.en_US
dc.description.collegeCollege of Scienceen_US
dc.description.departmentMathematics & Statisticsen_US
dc.format.extent54 pagesen_US
dc.identifier.urihttps://hdl.handle.net/1969.6/97721
dc.language.isoen_USen_US
dc.rightsThis material is made available for use in research, teaching, and private study, pursuant to U.S. Copyright law. The user assumes full responsibility for any use of the materials, including but not limited to, infringement of copyright and publication rights of reproduced materials. Any materials used should be fully credited with its source. All rights are reserved and retained regardless of current or future development or laws that may apply to fair use standards. Permission for publication of this material, in part or in full, must be secured with the author and/or publisher., This material is made available for use in research, teaching, and private study, pursuant to U.S. Copyright law. The user assumes full responsibility for any use of the materials, including but not limited to, infringement of copyright and publication rights of reproduced materials. Any materials used should be fully credited with its source. All rights are reserved and retained regardless of current or future development or laws that may apply to fair use standards. Permission for publication of this material, in part or in full, must be secured with the author and/or publisher.en_US
dc.subject2D ellpitical parabolic ODEen_US
dc.subjectfinite element methoden_US
dc.subjectfractional derivativesen_US
dc.subjectnumerical simulations & resultsen_US
dc.subjectpartial differential equationen_US
dc.titleNumerical investigation of the population distribution in heterogenous domainen_US
dc.typeTexten_US
dc.type.genreThesisen_US
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas A & M University--Corpus Christien_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Scienceen_US

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