پديد آورنده :
محمدي، مريم
عنوان :
روش هاي مبتني بر فضاي هيلبرت هسته بازتوليد در حل معادلات با مشتقات جزيي
گرايش تحصيلي :
آناليز عددي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
نه،174ص.: مصور،جدول،نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
رضا مختاري
استاد مشاور :
فريد بهرامي
تاريخ نمايه سازي :
23/1/93
استاد داور :
اسماعيل بابليان، نبي الله گودرزوند چگيني، مهدي تاتاري
كد ايرانداك :
ID600 دكتري
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
The methods for solving partial di erential equations on the basis of the reproducing kernel Hilbert space Maryam Mohammadi m mohammadi@math iut ac ir January 2014 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Reza Mokhtari mokhtari@cc iut ac ir Advisor Dr Farid Bahrami fbahrami@cc iut ac ir Department Graduate Program Coordinator Dr Farid Bahrami fbahrami@cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran AbstractThis thesis deals with the methods for solving partial di erential equations PDEs on thebasis of the reproducing kernel Hilbert space RKHS These methods are classi ed intosymbolic and numerical ones We applied symbolic methods for solving the generalizedregularized long wave GRLW equation nonlinear di erential di erence equations inverseproblems with nonlocal boundary conditions a class of nonlinear systems of PDEs andone dimensional nonlinear Schr dinger equation The numerical methods were also used ofor solving two dimensional nonlinear coupled Burgers equations and Brusselator reaction di usion system KeywordsPartial di erential equations reproducing kernel Hilbert space 1 IntroductionThe theory of reproducing kernels 1 3 was used for the rst time at the beginning of the20th century by Zaremba in his work on boundary value problems for harmonic and bihar monic functions In 1907 he was the rst who introduced in a particular case the kernelcorresponding to a class of functions and stated its reproducing property But he did not de velop any theory and did not give any particular name to the kernels he introduced In 1909 Mercer examined the functions which satisfy reproducing property in the theory of integralequations developed by Hilbert and he called these functions as positive de nite kernels Heshowed that these positive de nite kernels have nice properties among all continuous kernelsof integral equations However for a long time these results were not investigated Thenthe idea of reproducing kernels appeared in the dissertations of three Berlin mathematiciansSzeg 1921 Bergman 1922 and Bochner 1922 In particular Bergman introduced repro oducing kernels in one and several variables for the class of harmonic and analytic functionsand he called them kernel functions In 1935 Moore examined the positive de nite ker nels in his general analysis under the name of positive Hermitian matrix Later the theory
استاد راهنما :
رضا مختاري
استاد مشاور :
فريد بهرامي
استاد داور :
اسماعيل بابليان، نبي الله گودرزوند چگيني، مهدي تاتاري
