Journal of Mathematics and Statistics

An Improved Positivity Preserving Odd Degree-N Said-Ball Boundary Curves on Rectangular Grid Using Partial Differential Equation

Ahmed Kherd, Azizan Saaban and Noraziah Haji Man

DOI : 10.3844/jmssp.2016.34.42

Journal of Mathematics and Statistics

Volume 12, Issue 1

Pages 34-42


This paper discusses the sufficient conditions for positivity preserving odd degree-n Said-Ball boundary curves defined on a rectangular grid. We derive a sufficient condition on boundary curves of rectangular Said-Ball patches where the lower bound ordinates are adjusted independently. To construct the boundary curves for each rectangular patch, the Said-Ball polynomial solution of fourth order PDE will be considered where its coefficients can be calculated using edge Said-Ball ordinates which fulfill the positivity preserving conditions. Graphical examples are presented using well-known test functions.


© 2016 Ahmed Kherd, Azizan Saaban and Noraziah Haji Man. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.