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Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems.Model Reduction and Approximation: Theory and Algorithms:contains three parts that...

The book concerns theoretical and numerical aspects of systems of conservation laws, which can be considered as a mathematical model for the flows of inviscid compressible fluids.
Five leading specialists in this area give an overview of the recent results, which include: kinetic methods, non-classical shock waves, viscosity and relaxation methods, a-posteriori error estimates, numerical schemes of higher order on unstructured grids in 3-D, preconditioning and symmetrization of the Euler and Navier-Stokes equations.
This book will prove to be very useful for scientists working in...