شماره راهنما :
1482 دكتري
پديد آورنده :
حسيني، رسول
عنوان :
روش‌هاي جداسازي قطري براي حل رده‌اي از معادلات با مشتقات پاره‌اي
گرايش تحصيلي :
آناليز كاربردي
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
صفحه شمار :
دوازده، 93ص. : مصور، جدول، نمودار
استاد راهنما :
مهدي تاتاري
توصيفگر ها :
روش‌هاي جداسازي , معادلات با مشتقات پاره‌اي سهموي , معادلات با مشتقات پاره‌اي هذلولوي , روش جداسازي قطري , معادله برگرز , مدل اشنكنبرگ , اصل ماكزيمم
استاد داور :
محمد حسيني، اكبر محبي، حميدرضا ظهوري زنگنه
تاريخ ورود اطلاعات :
1398/08/18
تاريخ ويرايش اطلاعات :
1398/08/19
چكيده انگليسي :
Diagonal splitting methods for solving a class of partial di erential equations Rasool Hosseini Rasool hosseini@math iut ac ir September 17 2019 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mehdi Tatari mtatari@cc iut ac ir Advisor Dr Majid Gazor mgazor@cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranAbstractNowadays problems that naturally have a number of inherent geometrical properties are of greatinterest and the numerical methods used to solve such problems must be chosen in such a waythat the resulting solution preserves these properties These types of methods are called struc ture preserving methods Splitting methods are one of the most widely used methods amonggeometric integrators which are often used to overcome the complexity of computing problems constructing accurate high order numerical algorithms and extension of the region of stabilityof methods These ideas are used to overcome the computational complexity which is arisen innumerical solution of higher dimensional problems In this thesis a new splitting technique isimplemented for solving parabolic and hyperbolic PDEs As the main result the new meth ods preserve the maximum principle unconditionally or with a mild condition on discretizationparameters in comparison with well known methods Damping of numerical solution in time evo lution is investigated For numerical solution of the Burgers equation as a nonlinear problem an iterative method based on the new splitting technique is presented Key Words Splitting methods Hyperbolic PDE s Parabolic PDE s Diagonal Splitting method Burgers equation Schnakenberg Model Maximum principle MSC 2010 65L12 65M06 1
استاد راهنما :
مهدي تاتاري
استاد داور :
محمد حسيني، اكبر محبي، حميدرضا ظهوري زنگنه
