616 13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics13.42 a.Write a computer program to integrate the three
simultaneous differential equations for the
Lotka–Volterra mechanism of Equation (13.3-11)
using Euler’s method.^47 Assume that the
concentration of A is kept fixed. Make your value of
∆tsmall enough for adequate accuracy. Run the
program for several different sets of values of the
initial concentrations and the rate constants. Try to
determine how the behavior depends on these values.
(^47) R. G. Mortimer,Mathematics for Physical Chemistry, 3rd ed.,
Academic Press, San Diego, 2005, p. 260ff.
b. Determine the period of the oscillation for one or
more of your sets of initial conditions.
c.Using the Runge–Kutta method,^48 write a computer
program to integrate the differential equations of
part a. Run the program for some of the same sets of
values as used in part a to test the accuracy of the
Euler method.
(^48) R. G. Mortimer,loc. cit., p. 261; R. L. Burden and J. D. Faires,
Numerical Analysis, 4th ed., Brooks/Cole, Pacific Grove, CA, 2001.