MATHEMATICAL ANALYSIS AND NUMERICAL METHODS FOR SCIENCE AND TECHNOLOGY. - Volume 5, Evolution Problems I

Volumes 5 and 6 examine evolution (i.e. time-dependent) problems. The methods presented are useful for physics and mechanics (Chapter XV) as well as electronics, automata theory and robotics, etc. (Chapter XVI). In Chapter XVII it is shown that for a large class of problems the solution may be expressed in terms of a family (or semi-group) of time-dependent operators. Chapter XVIII deals with variational methods which are the simplest and the most powerful methods applicable to both non-symmetric and time-dependent operators, and form a basis for the study of nonlinear problems. The linearised Navier-Stokes equations are considered in Chapter XIX with particular variational methods. Chapter XX presents the methods of computation for evolution problems, serving as a basis for the effective calculation of evolutions on computer. The final chapter presents the many important and specific properties of the operator of transport equations.