One hundred differential equations execute directly on the IBM PC

Abstract

Inexpensive personal computers (IBM PC/XT/AT and compatibles) can do very respectable dynamic-system simulations at remarkable speed, as shown in this brief technical note. The direct-executing ENHANCED DESIRE system solves up to one hundred ordinary differential equations typed and edited on the CRT screen, without noticeable delay for program translation. Monochrome or color graphics are produced.Many simulation professionals may not realize that ordinary, quite inexpensive personal computers can do very respectable number-crunching if they are equipped with 8087 or 80287 math co-processors. Also, one needs software carefully designed to utilize the co-processors stack-machine architecture. This is especially true for newer PC and AT clones equipped with 7 or 8 MHz clocks. Such machines, which may retail for less than $2000, can match the simulation speed of a DEC PDP-11/44 minicomputer with hardware floating-point arithmetic and can solve much larger problems. Figure 1 depicts an example. Each link of this textbook delayline circuit may be described by a pair of first-order differential equations defining the delay-line capacitances and inductances. The straightforward computer program (see Appendix) lists the one hundred differential equations for a 50-link delay line in the DYNAMIC segment and specifies circuit parameters and a step-input amplitude vS = 1 Volt. The program then calls for a run-and-reset (drunr) with the termination resistance rL = 50 ohms, equal to the delay-line characteristic impedance, and Figure 1. Classical delay-line circuit (see, e.g., G.A. Korn, and JV. Wait, Digital Continuous-system Simulation, Prentice-Hall, Englewood, New Jersey, 1978).Figure 2. Epson screen prints for the delay-line response with matched and unmatched termination, taken from an ordinary 640 by 200 monocolor PC display.

A new software technique for sub-model invocation

“…DARE/ELEVEN (Korn and Wait 1978) was an example of a simulation system including such a macro generator. If the simulation language system has a sort mechanism (Korn and Wait 1978), then macro-generated model equations will be sorted, together with the rest of the model, just as if they had been entered by hand, and the simulation-language translation proceeds.DIRECT-EXECUTING SIMULATION Sub-model invocation is useful, but your macro-generating FORTRAN-based CSSL must now implement four separate operations before it can even begin to solve a differential equation: macro generation translation into FORTRAN FORTRAN compilation Linking By contrast, a direct-executing simulation system like EN-HANCED DESIRE (IBM PC/XT/AT and compatibles) or DESCTOP (VAX/MICROVAX) (Korn 1986(Korn , 1987) may finish several simulation runs while a FORTRAN-based system is still linking. A direct-executing system combines a compiler and an interpreter to execute the simulation.…”

“…DIRECT-EXECUTING SIMULATION Sub-model invocation is useful, but your macro-generating FORTRAN-based CSSL must now implement four separate operations before it can even begin to solve a differential equation: macro generation translation into FORTRAN FORTRAN compilation Linking By contrast, a direct-executing simulation system like EN-HANCED DESIRE (IBM PC/XT/AT and compatibles) or DESCTOP (VAX/MICROVAX) (Korn 1986(Korn , 1987) may finish several simulation runs while a FORTRAN-based system is still linking. A direct-executing system combines a compiler and an interpreter to execute the simulation.…”

“…Such a macro is then &dquo;invoked&dquo; in the DYNAMIC program segment with a statement like This macro call must generate in-line code for the sub-model equations, with the dummy parameters z, x, y, a, b correctly replaced by the actual model parameters Z, X, Y, A, B: This is a text-processing operation and requires a macro generator program, which makes an extra preliminary pass over the simulation source program. DARE/ELEVEN (Korn and Wait 1978) was an example of a simulation system including such a macro generator. If the simulation language system has a sort mechanism (Korn and Wait 1978), then macro-generated model equations will be sorted, together with the rest of the model, just as if they had been entered by hand, and the simulation-language translation proceeds.…”

“…DARE/ELEVEN (Korn and Wait 1978) was an example of a simulation system including such a macro generator. If the simulation language system has a sort mechanism (Korn and Wait 1978), then macro-generated model equations will be sorted, together with the rest of the model, just as if they had been entered by hand, and the simulation-language translation proceeds.…”

“…After the simulation run, the interpreter continues the expenment with a fast Fourier transformation of the array X and produces a frequency-response plot. commands (Korn (1986) which can readily call a macro generator (or any other pre-processor) without ever leaving the directexecuting program. Macro generation, though, still requires file manipulation, which takes some extra time even if we use a RAMdrive.…”