We describe a collection of test problems which have been used to develop and test data fitting software for identifying parameters in explicit model functions, dynamical systems of equations, Laplace transformations, systems of ordinary differential equations, differential algebraic equations, or systems of one-dimensional time-dependent partial differential equations with or without algebraic equations. The test cases are useful also for any other reasons, e.g., in experimental design, identification, or optimal control. In addition, they might facilitate the implementation of new solvers for integrating ordinary or partial differential equations. All test problems and the corresponding data sets can be downloaded from the home page of the author. They were collected when implementing the interactive data fitting program EASY-FIT ModelDesign, which is also available. All nonlinear model functions are implemented in a special modeling language called PCOMP providing function values and first and second partial derivatives. The corresponding Fortran codes of PCOMP are part of the software and data package.
Report, Department of Computer Science, University of Bayreuth, 95440 Bayreuth, Germany