From the reviews: “This book contains the basic concepts for the approximation of differential equations which arise in the mathematical modeling of real life applications. … it can be used as a textbook for graduate-level courses. Moreover, the interested reader can find a lot of information on the various aspects of the numerical approximation of differential problems, so that it can also be used as a starting point for the study of more specific topics in this field.” (Lucia Gastaldi, Mathematical Reviews, Issue 2010 h)
In this text, we introduce the basic concepts for the numerical modelling of partial equation differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also others, such as the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws. Furthermore, we provide numerous physical examples which underlie such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods.In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs in the MATLAB language. It is suitable for students of bachelor and master courses in scientific disciplines (engineering, mathematics, physics, computational sciences and information science), and recommendable to researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.