Numerical Integration of Partial Differential Equations

Abstract

A very large range of efficient techniques are exposed for solving partial differential equations. Various physical systems illustrate the different PDEs. The mathematical characterization of PDEs is explained. The method of characteristics is exposed by means of physical examples. The finite differences are very detailed with many different schemes and applications in heat and mass transfer and transport in 1D and 2D. Automatic finite differences and irregular grids are commented. Spectral methods, including Galerkin’s and collocations, radial basis functions, are explained with applications on ODEs and PDEs. A moving grid is detailed with application on a realistic chromatography. The finite volumes are detailed in 1D with application in heat and mass transfer. The finite elements are also explained with their foundations and algorithms, with many applications especially in heat transfer up to 3D. The boundary element method is treated in detail with application in heat transfer up to 2D. All these methods are explained mathematically and illustrated numerically with physical examples.