Analytic Advances in Difference Equations of Diffusion Processes

Beschreibung

This book is concerned with diffusion processes focusing on an underlying discrete scaling. More and more scientific articles appear which generalize mathematical models from partial differential equations to partial difference equations. This is also the native land of the mathematical methods used within the present book. It happens for two fundamentally different aspects of diffusion, namely diffusion of energy and material in the first part of the work, and diffusion of information in context of so-called opinion dynamics in the second part. Sciences as economy, biology, and physics often rely upon empirical data. Those are mostly pointwise given such as the growth of a bacteria colony at certain points of time. The traditional procedure provides a data mining by an interpolation of those to yield a continuous, universally valid equivalent of the observed reality. That a discrete version meets the demand was the undercarriage for a travel through the unfathomable world of mathematics. The generated discrete models from this book just reflect pointwise taken data and cause a direct production in terms of future assumptions. The operational expense for the evaluation can be controlled by a free choice of the length of time steps. This book shall not at least demonstrate that in particular nonlinearity though costly and painful evokes higher predictability of opinion formation and collective decision-making than conventional models.

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Maria Meiler

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Diffusion, Differnce Equations, Opinion Dynamics, Schrödinger equation, linear medel,

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