No abstract

The numerical stability of most finite difference schemes that are currently in use to attempt to numer-

-For evahration of arithmetical expressions using multiple precision floating-point arithmetic, a method is given to automatically perform error cumulation control prior to the actual computations.Individual errors and their effects are identified, and it is shown how to compute these effects efficiently via automatic differentiation.In the presented approach these effects we used to determine which precisiorrs have to be chosen during the real computations, in order to limit error cumulation to admissible, user chosen error bounds.

The structure of SIGSAM Problem #8, [1], motivated the development of algorithms to determine an arbitrary, say r-th, derivative with respect to t of a function f(t) α , where [EQUATION]

NETFORM is a very powerful and flexible tool for solving (sparse) systems of linear equations in algebraic form. The system includes convenient facilities to generate (and solve) linear equations for electrical networks.The accompanying Code Optimizer is a general purpose tool to automatically optimize sets of algebraic expressions, with emphasis on those generated by the NETFORM system.Thus the combination of both systems can be used to solve numerous problems of a symbolic and/or numeric nature, taking full advantage of the REDUCE 2 embedding in which it is supported.For instance NETFORM can automatically provide a user with descriptive (tableau) equations of an arbitrary linear electrical network and, as it solves such linear equations too, calculate any transferfunction of that linear electrical network. The NETFORM environment encourages users to think of electrical networks in terms of network elements, one port elements as well as subnetworks, which can be conveniently described and manipulated.Given a complete network description, NETFORM allows different approaches in analyzing it, i.e. a full symbolic analysis, a hybrid analysis, a state analysis or a mixed hybrid and state analysis.