الفهرس 
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Abstract
We studied three new forms for some relations of the eigenvalue of an elliptic PDE with NBCs and their corresponding eigenvectors. Several parameters are included in this new conditions such that for certain values of these parameters it can describe Dirichlet or Neuman conditions. The system of equations of the finite difference scheme is obtained and the boundary conditions are implemented in it. The matrix shows that the two points of NBCs inside the domain which yield a shift in the tridiagonal elements. 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 points out that it is more practical to propose the conditions in these general forms. We also note that, in some cases, the general relations are hard to obtain in a compact form. Also, we studied for the first time NSFD for elliptic PDEs with NBCs and some relations of the eigenvalues. where stability analysis for the difference scheme of this problem is affected by the two nonlocal conditions that affect the type and the value of eigenvalue, hence the corresponding eigenvectors. Finally, the results obtained from the relations in the one-dimensional problem for the nonlocal elliptic partial differential equations and nonstandard finite difference for an elliptic partial differential equation with nonlocal. In addition we use the separation of variables technique to generalized the two-dimensional problem.