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040 _aEG-GiCUC
_beng
_cEG-GiCUC
041 0 _aeng
049 _aDeposite
097 _aM.Sc
099 _aCai01.12.17.M.Sc.2014.Mu.N
100 0 _aMuner Mustafa Abouhasan
245 1 0 _aNumerical studies of di{uFB00}erential equations and their applications in financial mathematics /
_cMuner Mustafa Abou Hasan ; Supervised Laila F. Abdelal , Nasser H. Sweilam , Malak M. Rizk
246 1 5 _aدراسات عددية للمعادلات التفاضلية وتطبيقاتها في الرياضيات المالية
260 _aCairo :
_bMuner Mustafa Abou Hasan ,
_c2014
300 _a81 P. :
_bcharts ;
_c25cm
502 _aThesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics
520 _aThis thesis is a contribution on numerical solutions for systems of ordinary di{uFB00}erential equations (ODEs) and Black-Scholes parabolic partial di{uFB00}erential equations. Two di{uFB00}erent numerical approaches are presented in this thesis to solve general Black-Scholes equation. The {uFB01}rst one is: The modi{uFB01}ed Dzyadyk{u2019}s approximation iterative method (MDAI-metod) depending on Hermite poly- nomials, which is used to solve sti{uFB00} systems of ordinary di{uFB00}erential equations, then it is also used to solve parabolic partial di{uFB00}erential equations. Using MDAI method to solve partial di{uFB00}erential equations (PDEs) is facilitated by the method of lines which reduce the problem to solve a system of sti{uFB00} ordinary di{uFB00}erential equations. The stability analysis of this method is presented. The second method is: the non-uniform {uFB01}nite di{uFB00}erence method which is used to {uFB01}nd value of European and American put options using Black-Scholes Model. Stability of this method and the truncation error are studied here
530 _aIssued also as CD
653 4 _aBlack-Scholes equation
653 4 _aParabolic partial di{uFB00}erential equations
653 4 _aSystem of ordinary di{uFB00}erential equations
700 0 _aLaila Fahmy Abdelal ,
_eSupervisor
700 0 _aMalak M. Rizk ,
_eSuperviso
700 0 _aNasser Hassan Sweilam ,
_eSupervisor
856 _uhttp://172.23.153.220/th.pdf
905 _aEnas
_eCataloger
905 _aNazla
_eRevisor
942 _2ddc
_cTH
999 _c51643
_d51643