TY - BOOK ID - 36762253 TI - Numerical Models for Differential Problems PY - 2014 SN - 8847055210 8847055229 PB - Milano : Springer Milan : Imprint: Springer, DB - UniCat KW - Mathematics. KW - Mathematical analysis. KW - Analysis (Mathematics). KW - Applied mathematics. KW - Engineering mathematics. KW - Computer mathematics. KW - Numerical analysis. KW - Mathematical models. KW - Mathematics, general. KW - Analysis. KW - Numerical Analysis. KW - Mathematical Modeling and Industrial Mathematics. KW - Applications of Mathematics. KW - Computational Mathematics and Numerical Analysis. KW - Global analysis (Mathematics). KW - Computer science KW - Computer mathematics KW - Discrete mathematics KW - Electronic data processing KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Mathematical analysis KW - Math KW - Science KW - Mathematics KW - Differential equations, Partial KW - Numerical solutions. KW - Numerical analysis KW - Engineering KW - Engineering analysis KW - Models, Mathematical KW - Simulation methods KW - 517.1 Mathematical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:36762253 AB - 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. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. 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. ER -