Computer languages for numerical engineering problems

Abstract

Recent and anticipated advances in computer hardware capabilities have made hardware limitations insignificant for many numerical engineering problems. The difficulties of programming computers now constitute the greatest block to their effective utilization by engineers and scientists. Consequently, new languages that are specialized to numerical engineering problems are needed. Relmath is such a language. It is designed to solve ordinary differential equations and to manipulate the resulting functions. Systems of equations can be stated in a normal mathematical form and solved by a simple statement. Printed and plotted output can be readily obtained. Relmath also allows the definition of procedures for solving differential equations. Its procedural language is quite different from general programming languages. It is restricted to a certain class of algorithms, and the calculations that are common to all these methods are made implicit in the language. The language is highly supportive for procedures in this class. The user need only state the important mathematical steps, such as the formulas defining a Runge-Kutta scheme or the method of estimating the error, if error control is desired. Some considerations for the design and implementation of numerical engineering languages are discussed using Relmath as an example. The decisions involved in the design of Relmath are detailed. The behavior of a representative numerical algorithm in a paging environment is analyzed, which shows the importance of properly designing algorithms for such environments. Relmath's method of compiling its procedures is discussed. The compiled code is as fast as standard library subroutines. Finally, a plan for further research to develop a more supportive environment for the implementation of similar languages is outlined.