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Volume 13, Issue 3
A Convergence Analysis of Orthogonal Spline Collocation for Solving Two-Point Boundary Value Problems Without the Boundary Subintervals

B. Bialecki & R. I. Fernandes

Int. J. Numer. Anal. Mod., 13 (2016), pp. 383-402.

Published online: 2016-05

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  • Abstract

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.

  • Keywords

Two-point boundary value problem, orthogonal spline collocation, optimal order of accuracy.

  • AMS Subject Headings

65L10, 65L60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-383, author = {B. Bialecki and R. I. Fernandes}, title = {A Convergence Analysis of Orthogonal Spline Collocation for Solving Two-Point Boundary Value Problems Without the Boundary Subintervals}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {3}, pages = {383--402}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/445.html} }
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 -

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.

B. Bialecki and R. I. Fernandes. (2016). A Convergence Analysis of Orthogonal Spline Collocation for Solving Two-Point Boundary Value Problems Without the Boundary Subintervals. International Journal of Numerical Analysis and Modeling. 13 (3). 383-402. doi:
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