الفهرس Only 14 pages are availabe for public view
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Abstract
This 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