The Solution of Some Differential Equations by Nonstandard Finite Difference Method
| dc.contributor.advisor | Tanoğlu, Gamze | |
| dc.contributor.author | Kıran Güçoğlu, Arzu | |
| dc.date.accessioned | 2014-07-22T13:51:03Z | |
| dc.date.available | 2014-07-22T13:51:03Z | |
| dc.date.issued | 2005 | |
| dc.description | Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2005 | en_US |
| dc.description | Includes bibliographical references (leaves: 55-57) | en_US |
| dc.description | Text in English; Abstract: Turkish and English | en_US |
| dc.description | ix, 66 leaves | en_US |
| dc.description.abstract | In this thesis, the nonstandard finite difference method is applied to construct thenew finite difference equations for the first order nonlinear dynamic equation, second order singularly perturbed convection diffusion equation and nonlinear reaction diffusion partial differential equation The new discrete representation for the first order nonlinear dynamic equation allows us to obtain stable solutions for all step-sizes.For singularly perturbed convection diffusion equation, the error analysis reveals that the nonstandard finite difference representation gives the better results for any values of the perturbation parameters. Finally, the new discretization for the last equation is obtained.The lemma related to the positivity and boundedness conditions required for the nonstandard finite difference scheme is stated. Numerical simulations for all differential equarions are illustrated based on the parameters we considered. | en_US |
| dc.identifier.uri | https://hdl.handle.net/11147/3200 | |
| dc.language.iso | en | en_US |
| dc.publisher | Izmir Institute of Technology | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject.lcc | QA372 .K89 2005 | en |
| dc.subject.lcsh | Differential equations, Nonlinear--Numerical solutions | en |
| dc.subject.lcsh | Differential equations, Nonlinear | en |
| dc.subject.lcsh | Finite differences | en |
| dc.title | The Solution of Some Differential Equations by Nonstandard Finite Difference Method | en_US |
| dc.type | Master Thesis | en_US |
| dspace.entity.type | Publication | |
| gdc.author.institutional | Kıran Güçoğlu, Arzu | |
| gdc.coar.access | open access | |
| gdc.coar.type | text::thesis::master thesis | |
| gdc.description.department | Thesis (Master)--İzmir Institute of Technology, Mathematics | en_US |
| gdc.description.publicationcategory | Tez | en_US |
| gdc.description.scopusquality | N/A | |
| gdc.description.wosquality | N/A | |
| relation.isAuthorOfPublication.latestForDiscovery | cc750058-3946-4afb-a0bc-a6f980188af4 | |
| relation.isOrgUnitOfPublication.latestForDiscovery | 9af2b05f-28ac-4012-8abe-a4dfe192da5e |