13960

12687

كارشناسي ارشد

رياضي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

۱۳۹۷

هفت، ۷۶ص.: مصور، جدول، نمودار

محمدرضا احمدي (هيات علمي دانشگاه شهركرد)

مهدي تاتاري

اميرهاشمي

محمدرضا احمدي، رضا مزروعي

1397/07/18

كتابنامه

علوم رياضي

رياضي

ID12687

Numerical methods based on Magnusexpansion for linear differential equations Reyhaneh Mir r mir@math iut ac ir September 11 2018 Master of Science Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Mehdi Tatari mtatari@cc iut ac irAdvisor Dr Amir Hashemi amir hashemi@cc iut ac irMSC 2010 65L12 65L99 Key Words Higher order linear differential equation Nonautonomous coefficients Magnusexpansion Abstract Differential equations play an important role in modeling natural phenomena in sciences andengineering In this thesis numerical integrations based on Magnus expansion are investigatedfor linear differential equations Often differential equations possess qualitative properties thatwe are interested in being preserved under discretization of a numerical method This subjecthas been known under geometric numerical integration methods recently In this thesis weconsider differential equations in a Lie algebra The concepts of Lie algebras and Lie groupsare important tools to solve differential equations with symmetric methods A Lie group is adifferentiable manifold which is also a group and such the group product and the inverse map are differentiable Familiar examples of Lie groups are matrix Lie groups Very often thesolution of the initial value problem x f t x x 0 x0 evolves in a differentiable manifold by a Lie group i e in a homogeneous space Examples of homogeneous spaces are spheres tori and also Lie groups themselves Under such conditions it is certainly advantageous to build

مهدي تاتاري

اميرهاشمي

محمدرضا احمدي، رضا مزروعي