Designing software for one-dimensional partial differential equations

Users of software for solving partial differential equations are often surprised by its inability to formulate their problems. Computer scientists speak of partial differential equations (PDEs) as canonical coupled systems, typically in divergence form. Physicists, chemists, and engineers start with the same description, but then add real-world things like “Rankine-Hugoniot” conditions, integro-differential operators, and Eulerian (moving) coordinate systems. This paper describes a generalization of the classical PDE formulation that allows users to formulate virtually any pde problem. The extended formulation has been used successfully on a wide range of nontrivial problems in the physical sciences that cannot even be written down in the classical form.