Approximate computation of differential and integral operator's eigenvalues

Key Words: Eigenvalue, eigenfunction, symmetric operator, asymptotic behaviour Eigenvalue Problem is a key member and has a special role in Mathematics, Physics, Engineering and the other disciplines. In many problems eigenvalue represents critical force, may be potantial energy and critical frequency, etc. In spite of this importance, its rather than difficult to compute eigenvalues in some problems except in special structures . Therefore numerical solutions are revealed that made for obligation. It can be seen in finite dimension problems like Matrixs eigenvalue-eigenvector and difficulties for asymmetric matrixes could prove one?s worth. The same difficulties are seen in the problems of finite dimensions. On the other hand the techniques of approximation are useful in which estimate most important that smallest eigenvalue ? eigenvectors. Calculation of consecutive eigenvalues are instabil and results in wrong way. In this study, we will use variational methods and our operator will limit to differential operator. We will make an illustrate with the telling about method of Ritz and method of Minimax.