PARABOLIC EQUATION WITH PERIODIC CONDITION ON THE SO¬LUTION AND THE PROJECTION-DIFFERENCE METHOD OF ITS APPROXIMATE SOLUTION
Authors:
Type:
Article
Pages:
from 69
to 72
Status:
Published
Received:
29.08.2014
Accepted:
03.10.2014
Published:
03.10.2014
Language:
Russian
Keywords:
Hilbert space, parabolic equation, periodic condition, projection-difference method, time-implicit Euler’s method
Abstract (English):
Weakly soluble abstract linear parabolic equation with a periodic condition on the solution is solved approximately in the Hilbert space by the projection-difference method using time-implicit Euler’s method. Convergence of approx-imate solutions to the exact solution is obtained.
Weakly soluble abstract linear parabolic equation with a periodic condition on the solution is solved approximately in the Hilbert space by the projection-difference method using time-implicit Euler’s method. Convergence of approx-imate solutions to the exact solution is obtained.
Keywords:
Hilbert space, parabolic equation, periodic condition, projection-difference method, time-implicit Euler’s method
Hilbert space, parabolic equation, periodic condition, projection-difference method, time-implicit Euler’s method
Точная и приближенная задачи
Предполагается, что задана тройка сепарабельных гильбертовых пространств V⊂Η⊂V , где пространство V – двойственное к V , а пространство H отождествляется со своим двойственным H . Оба вложения плотные и непрерывные. При почти всех τ ∈[0,Τ] на ц ν ∈ V определены полуторалинейные формы α(t,u,v).
1. Lions Zh.-L., Madzhenes E. Neodnorodnye granichnye zadachi i ikh pri¬lozheniya. - M.: Mir, 1971. - 372 s.
2. Smagin V.V. Skhodimost´ metoda Galerkina priblizhennogo reshe¬niya parabolicheskogo uravneniya s periodicheskim usloviem na reshenie. Vestnik VGU. Seriya: Fizika. Matematika. - 2013. - № 1. - S. 222 - 231
