A method for solving differential equations via approximation theory

摘要

We consider the method of quasi-reversibility for numerical solving boundary-value problems for differential equations. A specific feature of our approach is the well posedness of the problems we study. We illustrate the main idea of the method with several examples of typical problems of mathematical physics. In particular, we propose a new idea for solving quantum-mechanical Schrödinger eigenvalue problems in many spatial dimensions based on the classical Korobov approximations.