A conversational Eigenanalysis program for solving differential equations

Dynamic models that arise in health physics applications are often expressed in terms of systems of ordinary differential equations. In many cases, such as box models that describe material exchange among reservoirs, the differential equations are linear with constant coefficients, and the analysis can be reduced to the examination of solutions of initial-value problems for such systems. This paper describes a conversational code, DIFSOL, that permits the user to specify the coefficient matrix and an initial vector of the system; DIFSOL prints out closed-form solutions [i.e., expressed as linear combinations of terms of the form e-/sup at/, e-/sup at/cos bt, and e-/sup at/sin bt] and tables of the solution, its derivative, and its integral for any specified linear combination of state variables. The program logic permits menu-driven control. The authors have operated a FORTRAN IV version of the code on a DEC PDP-10 for several years. A translation into BASIC has proved practical on Radio Shack TRS-80 Model I and III personal computers for smaller systems of differential equations (<12 state variables). The paper includes illustrations of the use of DIFSOL in studying metabolic models