الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The finite difference method for solving initial-boundary value
problems for partial differential equations is an approximate method, in
the sense that derivatives at a point are approximated by difference
quatients over a small interval , and we apply the new modified
technique for solving the initial-Boundary value problem of parabolic
type • This method is based on the construction of some integral
constraints and using lagrange multip.lier to minimize the local
truncation error vector norm •
In Chapter I, we introduced advanced concepts form the theory
of partial differential equations such as existence, uniqueness of
solutions, well posed and ill-posed problems and the classification of
equations and the associated initial and boundary conditions, with
physical examples.
In Cha pter II, The concepts of the [mite difference method is
introduced, and we have considered three methods for developing
difference equations, Taylor-series method, the integral method and the
method of polynomial fitting . Considering the associated discretization
and rounding errors, the convergence, stability and consistency.
In Chapter III, we propose a.new method for solving the initial
boundary value problem of parabolic type as a modified numerical
methods by using certain integral constraints in order to minimize and
estimate the local tnmcation error vector norm •