TY - JOUR
T1 - Convergence Analysis of ADI Orthogonal Spline Collocation Without Perturbation Terms
AU - Bialecki , Bernard
AU - Fernandes , Ryan I.
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 620
EP - 641
PY - 2021
DA - 2021/08
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/19385.html
KW - Convergence, alternating direction implicit method, orthogonal spline collocation, perturbation terms.
AB - <p style="text-align: justify;">For the heat equation on a rectangle and nonzero Dirichlet boundary conditions,
we consider an ADI orthogonal spline collocation method without perturbation terms, to specify
boundary values of intermediate solutions at half time levels on the vertical sides of the rectangle.
We show that, at each time level, the method has optimal convergence rate in the $L^2$ norm in
space. Numerical results for splines of orders 4, 5, 6 confirm our theoretical convergence rates and
demonstrate suboptimal convergence rates in the $H^1$ norm. We also demonstrate numerically that
the scheme without the perturbation terms is applicable to variable coefficient problems yielding
the same convergence rates obtained for the heat equation.</p>