Muner Mustafa Abouhasan <br/><br/>
Numerical studies of dierential equations and their applications in financial mathematics /  
 دراسات عددية للمعادلات التفاضلية وتطبيقاتها في الرياضيات المالية 
Muner Mustafa Abou Hasan ; Supervised Laila F. Abdelal , Nasser H. Sweilam , Malak M. Rizk 
 - Cairo :   Muner Mustafa Abou Hasan ,   2014 
 - 81 P. :   charts ;   25cm 
<br/><br/>Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Mathematics 
<br/><br/> This thesis is a contribution on numerical solutions for systems of ordinary dierential equations (ODEs) and Black-Scholes parabolic partial dierential equations. Two dierent numerical approaches are presented in this thesis to solve general Black-Scholes equation. The rst one is: The modied Dzyadyks approximation iterative method (MDAI-metod) depending on Hermite poly- nomials, which is used to solve sti systems of ordinary dierential equations, then it is also used to solve parabolic partial dierential equations. Using MDAI method to solve partial dierential equations (PDEs) is facilitated by the method of lines which reduce the problem to solve a system of sti ordinary dierential equations. The stability analysis of this method is presented. The second method is: the non-uniform nite dierence method which is used to nd value of European and American put options using Black-Scholes Model. Stability of this method and the truncation error are studied here 
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<br/><br/><label>Subjects--Index Terms: </label>Black-Scholes equation Parabolic partial dierential equations System of ordinary dierential equations