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Mathematics | Numerical Models for Differential Problems

Numerical Models for Differential Problems

Series: MS&A, Vol. 8

Quarteroni, Alfio

2nd ed. 2014, XIX, 658 p.

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  • Author faces here the basic concepts for the numerical modeling of partial differential equations
  • An outstanding reference work in this branch of applied mathematics
  • In particular, the author discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs
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.

Content Level » Lower undergraduate

Keywords » PDE - analysis - numerical modelling

Related subjects » Analysis - Applications - Computational Science & Engineering - Mathematics

Table of contents / Preface 

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Distribution rights for India: Researchco Book Centre, New Delhi, India

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