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Both of the authors of this book are disciples and collaborators of
the Brussels school of thermodynamics. Their particular domain of
competence is the application of numerical methods to the many
highly nonlinear problems which have arisen in the context of
recent developments in the thermodynamics of irreversi ble
processes: stability of states far from equilibrium, search for
marginal critical states, bifwrcation phenomena, multiple
stationnary states, dissipative structures, etc. These problems
cannot in general be handled using only the clas sical and
mathematically rigorous methods of the theory of differential,
partial differential, and int grodifferential equations. The
present authors demonstrate how approximate methods, re lyi ng
usually on powerful computers, lead to significant progress in
these areas, if one is prepa red to accept a certain lack of rigor,
such as, for example, the lack of proof for the convergence of the
series used in the context of problems which are not self adjoint,
nor even linear. The results thus obtained must consequently be
submit ted to an exacting confrontation with experimental
observations. - Even though, the '1 imited information obtained
concerning the, often unsuspec ted, mechanisms underlying the
observed phenomena is both precious and frequently sufficient. This
information results from the properties of the trial functions best
suited to the constraints of the problem such as the initial,
boundary, and "feedback" conditions, and the analysis of their
behavior in the course of the evolution of the system."
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