TITLE:
L-Stable Block Hybrid Second Derivative Algorithm for Parabolic Partial Differential Equations
AUTHORS:
Fidele Fouogang Ngwane, Samuel Nemsefor Jator
KEYWORDS:
Hybrid Second Derivative Method; Off-Step Point; Parabolic; Partial Differential Equations
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.2,
March
25,
2014
ABSTRACT: An L-stable block method
based on hybrid second derivative algorithm (BHSDA) is provided by a continuous
second derivative method that is defined for all values of the independent
variable and applied to parabolic partial differential equations (PDEs). The
use of the BHSDA to solve PDEs is facilitated by the method of lines which
involves making an approximation to the space derivatives, and hence reducing
the problem to that of solving a time-dependent system of first order initial
value ordinary differential equations. The stability properties of the method
is examined and some numerical results presented.