TY  - JOUR
AU  - Kherd, Ahmed 
AU  - Saaban, Azizan 
AU  - Man, Noraziah Haji 
PY  - 2016
TI  - An Improved Positivity Preserving Odd Degree-N Said-Ball Boundary Curves on Rectangular Grid Using Partial Differential Equation
JF  - Journal of Mathematics and Statistics
VL  - 12
IS  - 1
DO  - 10.3844/jmssp.2016.34.42
UR  - https://thescipub.com/abstract/jmssp.2016.34.42
AB  - 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.