Numerical models for differential problems
著者
書誌事項
Numerical models for differential problems
（MS&A, v. 2）
Springer, c2009
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注記
Includes bibliographical reference (p.581-593) index
内容説明・目次
内容説明
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
目次
A brief survey on partial differential equations.- Elements of functional analysis.- Elliptic equations.- The Galerkin finite element method for elliptic problems.- Parabolic equations.- Generation of 1D and 2D grids.- Algorithms for the solution of linear systems.- Elements of finite element programming.- The finite volume method.- Spectral methods.- Diffusion-transport-reaction equations.- Finite differences for hyperbolic equations.- Finite elements and spectral methods for hyperbolic equations.- Nonlinear hyperbolic problems.- Navier-Stokes equations.- Optimal control of partial differential equations.- Domain decomposition methods.- Reduced basis approximation for parametrized partial differential equations.
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