**RSIC COMPUTER CODE PSR-059**

**1. NAME AND TITLE**

MATEXP: Matrix Exponential Method Applied to Systems of Ordinary Differential Equations.

**2. CONTRIBUTOR**

Oak Ridge National Laboratory, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

Fortran IV; IBM 360/370.

**4. NATURE OF PROBLEM SOLVED**

The matrix exponential method of solving differential equations is a method of obtaining exact solutions for a set of constant coefficient, homogeneous differential equations. It is ideally suited to digital computation and is very simple to implement. It can give virtually exact solutions to systems of equations and is, therefore, of interest to many engineers engaged in systems analysis, automatic control, and simulation.

The matrix exponential method has also been implemented and used extensively in Fourier analysis
problems by simulating band-pass filters.

**5. METHOD OF SOLUTION**

**6. RESTRICTIONS OR LIMITATIONS**

None noted.

**7. TYPICAL RUNNING TIME**

On an IBM 7090 computer, a 59 x 59 system run for 1000 time steps took 10 minutes and an 8 x
8 run for 10,000 steps took 1.5 minutes. The solution time factor will vary from about 2 x 10^{-6} to 7
x 10^{-6}, depending on the amount of extra subroutine computation and printout, and will be
approximately halved for homogeneous equations.

**8. COMPUTER HARDWARE REQUIREMENTS**

MATEXP is operable on the IBM 360/370 computers. It uses about 22,000 words of core storage.

**9. COMPUTER SOFTWARE REQUIREMENTS**

A Fortran IV compiler is required.

**10. REFERENCE**

S. J. Ball and R. K. Adams, "MATEXP, A General Purpose Digital Computer Program for
Solving Ordinary Differential Equations by the Matrix Exponential Method," ORNL-TM-1933 (August
30, 1967).

**11. CONTENTS OF CODE PACKAGE**

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

**12. DATE OF ABSTRACT**

February 1984.

**KEYWORD: ** DIFFERENTIAL EQUATIONS SOLVING