Designing Software for One Dimensional Partial Differential Equations.

Users of software for solving partial differential equations are frequently surprised by its inability to even formulate their problems, let alone solve them. Computer scientists speak of partial differential equations ( pdes ) as canonical coupled systems, usually in divergence form. Physicists, chemists and engineers usually 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 non-trivial problems in the physical sciences that can not even be written down in the classical form.