ABSTRACT
Mathematical physics is a fundamental language of modern science, and one of its most powerful tools. This importance was clear to the genius Galileo nearly four centuries ago, and is commonly understood. All branches of classical mathematical physics like acoustics, elasticity, heat conduction, hydrodynamics, magnetics, metereology, oceanography, atomic physics, and engineering provide many important and often difficult mathematical problems. Similar equations are encountered very often in the relatively new mathematical branches of chemistry, biology, medicine, sociology, and ecology. The solution of this famous problem of Hilbert turned out to be a rather complicated matter, and had taken a number of decades more and the efforts of many outstanding mathematicians to be clearly understood. One of the numerical methods of fundamental theoretical importance, and at the same time serving as a key structure of many modern and widely used computational algorithms, is the Rayleigh-RUz method.
