An implementation of numerical algebraic methods of solving a stationary one-dimensional Schrödinger equation (SODSE) is presented. In the framework of the proposed approach, SODSE is converted into an algebraic eigenvalue problem, which represents a discrete version of studied problem on an equally spaced grid. The AMSSE program written in Delphi calculates eigenvalues and corresponding eigenvectors by means of various methods and algorithms described here. It is an efficient and valuable computational environment, which can be used in science and nanotechnology. Arbitrary potentials can be introduced into AMSSE program in the form of analytic formulae or data tables, or with the mouse. The user-friendly graphical interface takes advantage of full capabilities of the Windows operating system. Main program features are described. Efficiency and accuracy of different numerical algorithms are comprehensively tested and compared. Factors influencing accuracy are discussed. Examples are widely presented. Matrix approach extension to the case of an effective-mass equation is mentioned.