An Exponential Method for the Solution of
Systems of Ordinary Differential Equations 

An explicit, coupled, single-step method for
the numerical solution of initial value problems 
for systems of ordinary differential equations is presented.
 The method was designed to be general purpose 
in nature but to be especially efficient when dealing
with stiff systems of differential equations.  
It is, in general, second order except for the case
of a linear system with constant coefficients and 
linear forcing terms; in that case, the method is third
order.  It has been implemented and put to routine 
usage in biological applications-where stiffness frequently
appears-with favorable results.  When compared 
to a standard fourth order Runge-Kutta implementation,
computation time required by this method has ranged 
from comparable for certain nonstiff problems to better
than two orders of magnitude faster for some 
highly stiff systems.

CACM December, 1974

Chu, S. C.
Berman, M.

numerical solution, ordinary differential equations,
initial value problems, stiff systems

5.17

CA741207 JB January 13, 1978  4:20 PM

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