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A Radial Basis Function Generated Finite-Differences (RBF-FD) inspiredtechnique for evaluating definite integrals over the volume of the ball inthree dimensions is described. Such methods are necessary in many areas ofApplied Mathematics, Mathematical Physics and many other application areas.Previous approaches needed restrictive uniformity in the node set, which thealgorithm presented here does not require. By using RBF-FD approach, theproposed algorithm computes quadrature weights for $N$ arbitrarily scatterednodes in only $O(N\mbox{ log}N)$ operations with high orders of accuracy.

Approximation of Definite Integrals Over the Volume of the Ball