PDEeksempler

PDEeksempler is a Danish term used in mathematics education to refer to collections or repositories of partial differential equation examples. The aim is to illustrate common types of PDEs, solution techniques, and the interplay between theory and computation. Such resources appear in lecture notes, textbooks, online courses and university problem sets, and may be organized by topic, method, or application.

Typical PDEeksempler cover the three broad classes of linear PDEs: elliptic equations such as Laplace’s equation ∇²u = 0 and Poisson’s equation ∇²u = f; parabolic equations such as the heat equation ∂t u = α∇²u; and hyperbolic equations such as the wave equation ∂²t u = c²∇²u. Problems are usually posed as boundary value problems or initial value problems, with Dirichlet, Neumann, or Robin boundary conditions.

Solutions in these collections show analytical methods like separation of variables, Fourier series, and Green’s functions, as well as numerical approaches including finite difference, finite element, and spectral methods. They may also illustrate qualitative tools based on energy estimates and characteristics.

PDEeksempler are used to illustrate modeling choices, stability considerations, and the interpretation of results in physics, engineering, and environmental science. They often include worked examples, diagrams, and, where available, sample code to reproduce computations.