الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
We studied elliptic PDE with three new forms that we proposed for multipoint conditions. These conditions work as generalizations to the already known ones. The system of equations of the finite difference scheme is obtained and the boundary conditions are implemented in it. When we studied the difference eigenvalue problem for these problems, we end up with general relations that describe not only the considered problems, but other problems as well in limit forms. This point out that it is more practical to propose the conditions in these general forms. But we also note that, for some cases, these general relations are hard to obtain in compact form.Parabolic PDE with integral condition is also considered. The integral conditions are also formed as generalizations of the classical ones. The difference eigenvalue problem is analyzed hence the stability conditions of the implicit and explicit difference schemes are given. These integral conditions can be thought of as an intermediate forms of conditions. If the limits of the integrals are allowed to change with time, this transforms the problem from one model to another via changing the boundary conditions.A weakly-singular PIDE is approximated via Taylor series of first order to a PDE with variable coefficients. The stability analysis for the difference scheme of this problem is affected by the multipoint nonlocal condition that affects the eigenvlaues of the difference scheme. It is also affected by the fact that the coefficients of the difference system of equations is now a function of time. We deduce the stability condition for both implicit and explicit schemes.We consider parabolic PIDEs with nonlocal conditions. As far as we know, this is the first attempt to tackle the difference eigenvalue problem and stability of such problems. Due to the integral of the unknown function in the equation, the difference scheme is variable multilayer scheme. We related the satbility condition for the difference system of this problem with the stability condition of the transition matrix of a classical parabolic PDE. This enables the researchers to apply this criterion of stability analysis to this type of problems with different difference schemes.