G-Spline Interpolation for Approximating the Solution of the Ordinary Differential Equations Using Linear Multistep Methods.

The main objectives of this thesis, is oriented toward function approximation using special type of spline functions, which is called the “Gspline “including the details of the subject. The second objective consider the 1st  order ordinary differential equations of the form: .
y'(x)=F(x,y),   x ∈[a,b]

y(a)=y 0 ,
Where the study concern the approximate solution of the above differential equation using linear multistep methods based on G-spline interpolation and then a generalization to this approach have been extended to solve Boundary value problems of the second order ordinary differential equations.