Ìàòåìàòèêà/5. Ìàòåìàòè÷åñêîå ìîäåëèðîâàíèå
Baimankulov A.
Kostanay State
University named after A.Baitursynov,
Kazakhstan.
Stability of the solution of the differencial problem
Consider the perturbed problem
If we
introduce the designations for the difference
,
get the equation
(1)
, (2)
ãäå 
=
perturbation of the initial condition 
, 
.
Multiplying
(1) on 
and summing over 
and 
get
.
For the
last term we use the formula of summation by parts
.
Applying
Cauchy-Bunyakovskii formula, we get
.
Arguing
as in previous works, we conclude that
.
Substituting
and applying the Gronwall lemma (differencial analogue) we obtain the estimate:
.
The
last inequality indicates the stability of the solution of the differencial
problem (1)-(2) given in [3].
That
is, a small change in the flow of moisture 
and the initial distribution of
moisture 
causes a small change in the
solution of the differencial problem (1)-(2) given in [3].
References
1.Òèõîíîâ À.Í., Ñàìàðñêèé À.À. Óðàâíåíèÿ
ìàòåìàòè÷åñêîé ôèçèêè. – Ì.: Íàóêà, 1996, 724 ñ.
2.Ðûñáàéóëû Á.
Èäåíòèôèêàöèÿ êîýôôèöèåíòà ïðîíèöàåìîñòè ïëàñòà ïðè óïðóãîì ðåæèìå äîáû÷è
íåôòè// Âåñòíèê ÊÁÒÓ, 2008 ã., ¹2(5), ñ. 46-51.
3.Áàéìàíêóëîâ À.Ò. Êîíå÷íî-ðàçíîñòíàÿ
àïïðîêñèìàöèÿ ïðÿìîé è ñîïðÿæåííîé çàäà÷ // Materialy IX miedzynarodowej
naukowi-praktycznej konferencji «Europejska nauka XXI powieka-2013» Volume 27.
Matematyka. Fizyka. Budownictwo i architektura.: Przemysl. Nauka i studia -
C.22-23.