Journal
PHYSICA SCRIPTA
Volume 96, Issue 7, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1402-4896/abfba9
Keywords
radial basis function; Hermite; multiquadric RBF; high order; weighting coe?cients
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Funding
- Deanship of Scientific Research at King Saud University [RG-1441-326]
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This paper investigates and optimizes the order of approximation formulas on nonuniform grids using the RBF-HFD approach, resulting in new weighting coefficients with higher convergence rates. Theoretical discussions are supported with several tests to demonstrate the effectiveness of the method.
It is well known that the order of finite difference estimates on nonuniform grids reduce dramatically, particularly when higher order derivatives are required. This paper contributes how an optimization of the order of approximation formulas can be investigated and done on such grids for a sufficiently smooth function. To generalize the idea as well as get the optimized orders, the notion of radial basis function-Hermite finite difference (RBF-HFD) approach is used. The new weighting coefficients are worked out and proved to possess higher convergence rates. Several tests are also given to demonstrate the theoretical discussions.
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