Eléments d'équations aux dérivées partielles pour ingénieurs : théorie et méthodes numériques, 1 / C. Cuvelier, J. Descloux, J. Rappaz...[et al.]

The first ten chapters address stationary problems: Ordinary boundary value problems - Green's function, difference methods for their solution, variational methods, finite element methods, eigenvalue problems. Second order elliptic partial differenial equations - Dirichlet, Neumann and mixed boundary conditions, variational formulation, Green's function, finite element methods. Bessel functions with applications. Integral transforms (Fourier, Hankel, Laplace, Mellin) - definition, properties, inversion, examples and applications. Chapters 11 to 15 and 17 study evolutionary problems: Ordinary initial value problems - existence and uniqueness, difference equations, difference methods for first order explicit differential equations, stiff differential systems and stability regions. Second order linear parabolic equations - heat equation, maximum principle, abstract evolution equations and weak solutions, difference methods and stability, finite element method, discontinuous Galerkin methods. Linear hyperbolic equations and systems - wave equation, first order systems, difference methods, method of characteristics. Nonlinear hyperbolic equations and systems - conservation laws, Riemann's problem, numerical approximation with Godunov's method. In chapter 18 the Navier-Stokes equations and their numerical solution are discussed: difference methods, direct and penalized finite element methods. Nonlinear equations in several variables and the computation of their solutions is outlined in chapter 16 - Banach's fixed point theorem, Newton's method, nonlinear eigenvalue problems and continuation methods. The final chapter presents a survey on direct and iterative methods for the numerical solution of systems of linear equations. The presentation of this book is clear and easily readable. Most chapters include some exercises, each chapter is completed with a bibliography of important references. The work should serve excellently as a first guide to the investigation of mathematical properties of the solution of partial differential equations from physics and engineering and their numerical computation. (Zentralblatt)

Bibliogr.