پديد آورنده :
محرري، مهرزاد
عنوان :
حل عددي معادلات ديفرانسيل كسري با استفاده از تركيب توابع بلاك پالس و چند جمله اي هاي لژاندر
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده رياضي
صفحه شمار :
ده، 141ص: نمودار
يادداشت :
ص.ع:به فارسي و انگليسي
استاد راهنما :
حميد رضا مرزبان
توصيفگر ها :
حسابان كسري , توابع متعامد , ماتريس عملياتي , روش تاو , روش نقاط تركيبي
تاريخ نمايه سازي :
25/09/1392
استاد داور :
مهدي تاتاري، رضا مزروعي سبداني
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديحيتال
چكيده انگليسي :
Numerical Solution of Fractional Di erential Equations by Using Hybrid Block Pulse and Legendre Polynomials Mehrzad Mohareri m mohareri@gmail com 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid Reza Marzban hmarzban@cc iut ac ir Advisor Dr Reza Mokhtari mokhtari@cc iut ac ir 2010 MSC Keywords fractional caculus orthogonal function block pulse function legendre polynomial operational matrix AbstractMany real life phenomena can be modeled by fractional di erential equations Di erent types offractional di erential equations arising in various elds of science and engineering A great deal ofresearches has shown the advantageous use of the fractional calculus in the modeling and control ofmany dynamical systems In mechanics fractional calculus plays an important role for example it has been successfully employed to model damping forces with memory e ects to described state 1 3feedback controllers In particular order derivative or order derivative describe the frequency 2 2dependent damping materials satisfactorily Other examples are nonlinear oscillation of earthquakes uid dynamic tra c model continuum and statistical mechanics colored noise solid mechanics eco nomics bioengineering anomalous transport and dynamics of interfaces between nanoparticles andsubstrates Up to now many papers have been devoted to the theoretical aspects and numericaltreatments of fractional di erential equations The analytic results on the existence and uniquenessof solutions to the fractional di erential equations have been investigated by many authors In thisthesis an e cient and e ective approximation scheme is successfully developed for solving linear andnonlinear multi order fractional di erential equations The method is based on a hybrid of block pulsefunctions and the well known Legendre polynomials This type of hybrid functions constitutes a com plete orthogonal set in the Hilbert space L2 0 T The fractional operational matrices of integration
استاد راهنما :
حميد رضا مرزبان
استاد داور :
مهدي تاتاري، رضا مزروعي سبداني
