In this book, the eigenvalue problems for ordinary differential equation with boundary conditions is considered. We proposed the semi analytic technique to solve non - singular eigenvalue problems using osculator interpolation. The technique finds the eigenvalue and the corresponding nonzero eigenvector which represent the solution of the problem in a certain domain. Many applications in mathematical physics and electromagnetic or elastic wave equations, chemical reaction theory, radiative heat transfer and nanotechnology such the Mathieu differential equation and Bratu equation are presented.