TY - JOUR
T1 - The Crank-Nicolson Hermite Cubic Orthogonal Spline Collocation Method for the Heat Equation with Nonlocal Boundary Conditions
AU - Bialecki , B.
AU - Fairweather , G.
AU - Lόpez-Marcos , J. C.
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 442
EP - 460
PY - 2013
DA - 2013/08
SN - 5
DO - http://doi.org/10.4208/aamm.13-13S03
UR - https://global-sci.org/intro/article_detail/aamm/79.html
KW - Heat equation, nonlocal boundary conditions, orthogonal spline collocation, Hermite
cubic splines, convergence analysis, superconvergence.
AB - <p style="text-align: justify;">We formulate and analyze the Crank-Nicolson
Hermite cubic orthogonal spline collocation
method for the solution of
the heat equation in one space variable
with nonlocal boundary conditions involving integrals of
the unknown solution over the spatial interval.
Using an extension
of the analysis of Douglas and Dupont [23]
for Dirichlet boundary conditions,
we derive optimal order error
estimates in the discrete maximum norm in time
and the continuous maximum norm in space.
We discuss the solution of the linear system arising at each time level
via the capacitance matrix technique and the package COLROW
for solving almost block diagonal linear systems.
We present numerical examples that confirm the theoretical
global error estimates and exhibit superconvergence phenomena.</p>