The Fourier series, Laplace and Fourier transforms are applicable for the solution of parabolic type involutory differential problem with constant or polynomial coefficients. In the present paper, the first and second order of accuracy difference schemes for the numerical solution of the initial boundary value problem for one dimensional parabolic type involutory partial differential equation are presented. Numerical results are given.

1.
A.
Ardito
,
P.
Ricciardi
,
Nonlinear Analysis: Theory
,
Method & Applications
4
(
2
),
411
414
(
1980
).
2.
Delay Differential Equations and Applications
, Editors by
O.
Arino
,
M.L.
Hbid
,
E. Ait
Dads
(
Springer
,
Berlin
,
2006
).
3.
G.
Di Blasio
,
Nonlinear Analysis: Theory
,
Method & Applications
52
(
2
) (
2003
).
4.
V.V.
Vlasov
,
N.A.
Rautian
,
Spectral Analysis of Functional Differential Equations
(
MAKS Press
,
Moscow
,
2016
). (Russian).
5.
A.L.
Skubachevskii
,
Doklady Akademii Nauk
335
(
2
),
157
160
(
1994
).
6.
X.
Lu
,
Combined, Appl. Math. Comput
.
89
,
213
224
(
1998
).
7.
D.
Agirseven
,
Abstract and Applied Analysis
,
10
(
1155
),
682752
(
2012
).
8.
A.
Ashyralyev
,
D.
Agirseven
,
Modelling and Control
19
(
3
),
335
349
(
2014
).
9.
H.
Poorkarimi
,
J.
Wiener
,
Electronic Journal of Differential Equations Conference
02
,
87
91
(
1999
).
10.
A.H.
Bhrawy
,
M.A.
Abdelkawy
,
F.
Mallawi
,
Boundary Value Problems
,
2015
(
103
) (
2015
).
11.
V.
Borukhov
and
P.
Vabishchevich
.
Comput. Phys. Commun
126
,
32
36
(
2000
).
12.
R.
Nesbit
,
Delay Differential Equations for Structured Populations, Structured Population Models in Marine, Terrestrial and Freshwater Systems
(
Tuljapurkar & Caswell
,
ITP
,
1997
).
13.
A.
Ashyralyev
,
A. M.
Sarsenbi
,
Electronic Journal of Differential Equations
2015
(
284
),
1
8
(
2015
).
14.
A.
Ashyralyev
,
A. M.
Sarsenbi
,
Numerical Functional Analysis and Optimization
38
(
10
),
1295
1304
(
2017
).
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