TY - JOUR
T1 - A Convergence Analysis of Orthogonal Spline Collocation for Solving Two-Point Boundary Value Problems Without the Boundary Subintervals
AU - B. Bialecki & R. I. Fernandes
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 383
EP - 402
PY - 2016
DA - 2016/05
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/445.html
KW - Two-point boundary value problem, orthogonal spline collocation, optimal order of accuracy.
AB - <p style="text-align: justify;">We consider a new Hermite cubic orthogonal spline collocation (OSC) scheme to solve a
two-point boundary value problem (TPBVP) with boundary subintervals excluded from the given
interval. Such TPBVPs arise, for example, in the alternating direction implicit OSC solution of
parabolic problems on arbitrary domains. The scheme involves transfer of the given Dirichlet
boundary values to the end points of the interior interval. The convergence analysis shows that
the scheme is of optimal fourth order accuracy in the maximum norm. Numerical results confirm
the theoretical results.</p>