The
implementat
ion of the R
ichardson Extrapolat
ion
in comb
inat
ion w
ith d
ifferent numer
ical methods for solv
ing systems of ord
inary d
ifferent
ial equat
ions (ODEs)
is relat
ively s
imple, but the
important requ
irement for stab
il
ity of the computat
ional process may cause ser
ious d
iff
icult
ies. For example, the commonly used by sc
ient
ists and eng
ineers Trapezo
idal Rule has good stab
il
ity propert
ies, but
its comb
inat
ion w
ith the R
ichardson Extrapolat
ion
is unstable. Therefore,
it
is necessary to study
in advance and very carefully the stab
il
ity of the new numer
ical methods ar
is
ing when the sc
ient
ists and the eng
ineers use th
is computat
ional dev
ice
in comb
inat
ion w
ith d
ifferent algor
ithms for solv
ing systems of ODEs.
id="sp000065">We are presenting a systematic investigation of the implementation of Richardson Extrapolation for two implicit Runge–Kutta methods. Three numerical examples, including an atmospheric chemical scheme used successfully in several extensive environmental studies and described mathematically by a very stiff and badly scaled nonlinear system of ODEs, are presented to illustrate the advantages of the presented approach. The numerical results show that not only are the computations stable, but also the achieved accuracy is higher when the Richardson Extrapolation is additionally applied. It will be possible to derive similar stability and accuracy results for other implicit Runge–Kutta methods.