A system is presented to allow end users to solve nonlinear differential equations without need to write computer programs. The system treats n th order space (one dimensional), first order time systems with initial and/or two point boundary value specification. Users of the system need only enter the problem in direct mathematical notation, and output is automatically presented as a solution graph. The system allows the user to alter this equations, in-situ, that is to computationally steer his model. Thus the system is suited for model prototyping. Implementation is based on an object-oriented paradigm, well established and robust numerical procedures, and distributed computing to supported needed resources for numerically intensive tasks.

This paper describes the design of a scientific prototyping environment in Smalltalk and discusses implementation strategies to achieve high performance interactive modeling of computationally intensive physical problems. Classes for scientific visualization, including contour plotting and 3D surface representations which incorporate the model-view-controller paradigm are presented. Techniques for inclusion of user primitives written in C to support computationally intense methods are described in detail in their current implementation on advanced Smalltalk workstations (SUN4, Ardent Titan, Tektronix 4317).