**RSIC COMPUTER CODE PSR-078**

**1. NAME AND TITLE**

FORSIM VI: A Fortran-Oriented Simulation Package for the Automated Solution of Partial and
Ordinary Differential Equation Systems.

FORSIM was first conceived at an Atomic Energy of Canada Simulation Symposium held at
Sheridan Park Research Centre in 1971. The original FORSIM was a simple system for integration
of ordinary differential equations (ODE's), but this was followed by an extension to stiff equation
systems, partial differential equations (PDE's) in one space dimension, implicitly coupled PDE-ODE
systems, integration using sparse matrix techniques, two-dimensional PDE's and discontinuous
equations.

**2. CONTRIBUTOR**

Chalk River Nuclear Laboratories, Chalk River, Ontario, Canada.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV; CDC 175/6600.

**4. NATURE OF PROBLEM SOLVED**

FORSIM VI automates the solution of coupled differential equation systems. The independent
variables are time and up to three space coordinates, and the equations may be any mixture of partial
and/or ordinary differential equations. FORSIM VI provides a tool which will solve a system of
differential equations for a user who has basic but unspecialized knowledge of numerical analysis and
Fortran.

**5. METHOD OF SOLUTION**

The equations to be solved, together with the initial conditions and any special instructions, may be specified by the user in a single Fortran subroutine; a number of routines may be written if this method is more suitable. These are then loaded with the control routines which perform the solution and any requested input and output.

Partial differential equations are automatically converted into sets of coupled ordinary differential equations by variable order discretization in the spatial dimensions. These and other ordinary differential equations are integrated continuously in time using efficient variable order, variable step, error-controlled algorithms.

The mathematical routines are supplemented by flexible input/output facilities and a number of
utility routines commonly used in simulation.

**6. RESTRICTIONS OR LIMITATIONS**

While the algorithms used in FORSIM VI have been rigorously tested, and will reliably produce
solutions for correctly defined mathematical problems, the user must make certain that his equations
are mathematically correctly posed. Given an ill-defined mathematical statement of equations and
auxiliary constraints, any system of solution will produce a meaningless answer.

**7. TYPICAL RUNNING TIME**

No study has been made by RSIC of typical running times for FORSIM VI.

**8. COMPUTER HARDWARE REQUIREMENTS**

FORSIM VI was designed to be operable on the CDC 175/6600 computer. Basic FORSIM with room for 1000 equations requires about CM70000 (octal) to load and execute. As the user routines and any FORSIM library routines loaded will increase this slightly, default memory CM100000 (octal), or CM parameter on job card absent, was recommended for use at CRNL.

For jobs with a large number of equations using the sophisticated Hindmarsh/Gear/Carver/Reid
algorithm, more memory may be required. FORSIM will report on how much memory is needed after
the first, exploratory trial run.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A Fortran IV compiler is required.

**10. REFERENCE**

M. B. Carver, D. G. Stewart, J M. Blair, and W. N. Selander, "The FORSIM VI Simulation
Package for the Automated Solution of Arbitrarily Defined Partial and/or Ordinary Differential
Equation Systems," AECL-5821 (February 1978).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document and one (1.2MB) DOS diskette which contains the source
code, sample problem, and test problem JCL input.

**12. DATE OF ABSTRACT**

February 1984.

**KEYWORD: ** DIFFERENTIAL EQUATIONS SOLVING