الفهرس 
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Abstract
B-spline functions introduce a great importance in several science branches as in numerical analysis, ordinary and partial differential equations, integral equations and statistical analysis. They have also many applications in science, engineering, economics, biology and medicine, etc. In this thesis, we study cubic B-spline in calculating numerical solutions for second order parabolic partial differential equations. In addition, we use quartic B-spline in calculating numerical solutions for third order nonlinear partial differential equations. Moreover, sextic B-splines are used to solve fifth order partial differential equations. This thesis contains five chapters, and is organized as follows: Chapter I contains a survey of the previous studies related to this field. In chapter II, we consider the approximate solution of second order parabolic and hyperbolic equations known as Newell Segel type equation and Phi-four equation by using cubic B-spline method. A linear stability analysis is introduced using Von-Neumann method. The numerical results are compared with the exact solution. In chapter III, third order partial differential equations known as Gardner, Harry Dym and Jaulent Miodek coupled equations are solved using quartic B-spline. The stability of the proposed method for the solution is studied, and it was found that this method is unconditionally stable. The obtained results were very good compared to the results obtained from the exact solution.