الفهرس | Only 14 pages are availabe for public view |
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 • |