الفهرس 
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Abstract
In the present work, the linear parabolic initial-value problem
o,u-t:..u = I
IS considered JI1 the cylinder Qr = nx (0, T), where
n c RN (N = 1,2) is bounded. A fully discrete scheme is given
using CO -piecewise linear finite element in space and Rothe
scheme in time. The convergence of the proposed scheme and L2-
error estimate for the approximation of u is analyzed. Also, in this
’work a numerical approximation scheme for nonlinear nondegenerate
parabolic problems of the form
0, b( u ) - t:.. u = I
is presented. The algorithm is based on a nonstandard time
discretization scheme (the Jager and Kacur scheme) and the method
of lines. This leads to a very efficient and accurate procedure. The
stability and convergence of this method are proved.
Keywords: Time discretization methods, Rothe method,
Galerkin finite clement method, nonlinear non-degenerate parabolic
partial di [ferent ial equations, error estimates.