In this work, we study time-nonlocal boundary value problem for multi-dimensional parabolic partial differential equa- tion. Two difference schemes for approximate solution of non-local boundary value problem are discussed. Theorems on stability of solutions both difference schemes are given without proof. Numerical results for test examples are outlined.
Topics
Algebraic geometry
REFERENCES
1.
A.
Ashyralyev
, Journal of Evolution Equations
, 6
(1
) 1
–28
(2006
).2.
A.
Ashyralyev
and P.E.
Sobolevskii
, New Difference Schemes for Partial Differential Equations
(Birkhäuser Verlag
, Basel, Boston, Berlin
, 2004
).3.
A.
Ashyralyev
, A.
Hanalyev
and P.E.
Sobolevskii
, Abstract and Applied Analysis
6
(1
) 53
–61
(2001
).4.
A.
Ashyralyev
, I.
Karatay
and P.E.
Sobolevskii
, Discrete Dynamics in Nature and Society
, 2004
(2
) 273
–286
(2004
).5.
A. V.
Gulin
and V.A.
Morozova
, Differ. Equ.
39
(2
) 962
–967
(2003
).(in Russian).6.
I.P.
Gavrilyuk
and V.L.
Makarov
, Preprint Institut fur Angewandte Analysis und Stochastik(WIAS)
(Berlin
, 2000
).7.
8.
C.
Ashyralyyev
, e-Journal of Analysis and Applied Mathematics
, 2018
, No 1
11
–20
(2018
).9.
C.
Ashyralyyev
, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan
46
(2
) 346
–359
(2020
).10.
C.
Ashyralyyev
, Math. Meth. Appl. Sci.
43
5369
–5379
(2020
).11.
C.
Ashyralyyev
, P.
Akkan
, Numerical Functional Analysis and Optimization
41
(16
) 1913
–1935
(2020
).12.
C.
Ashyralyyev
, A.
Gonenc
, International Journal of Applied Mathematics
34
(2
), 273
–282
(2021
)13.
C.
Ashyralyyev
, A.
Dural
, Y.
Sozen
, Abstract and Applied Analysis, 294154
(2012
)14.
Y.G. and
M.
Oberguggenberger
, Journal of Mathematical Analysis and Applications
233
(2
) 644
–658
(1999
).15.
M.A.
Sadybekov
, e-Journal of Analysis and Applied Mathematics
, 2018
, No 1
1
–10
(2018
).16.
W.J.
Beyn
and B.M.
Garay
, Applied Numerical Mathematics
41
(3
) 369
–400
(2002
).17.
R.
Rautmann
, Nonlinear Analysis: Theory, Methods and Applications
, 30
(4
) 1915
–1926
(1997
).18.
Yu.A.
Smirnitskii
and P.E.
Sobolevskii
, The positivity of difference operators, Vychisl. Sist.
87
120
–133
(1981
) (in Russian).19.
A. E.
Polichka
and P.E.
Sobolevskii
, Trudy Mosk. Mat. Obshch.
36
29
–57
(1978
) (Russian).20.
V.V.
Shelukhin
, Sib. Math. J.
, 32
(2
), 309
–320
(1991
).21.
22.
23.
V. N.
Starovoitov
, Sib. Mat. Zurn.
62
(2
) 417
–421
(2021
).24.
25.
26.
P.E.
Sobolevskii
, Difference Methods for the Approximate Solution of Differential Equations
(Voronezh State University Press
, Voronezh
, 1975
) (in Russian).
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