Abstract
Radial basis functions are certain real-valued functions that depend only on the distance of their argument to a fixed point, i.e. x↦Ψ(∥x −x 0∥). Among them, one can find Gaussians, multiquadrics and, the subject of this paper, Wendland functions that are compactly supported and positive definite functions by Wendland (Adv Comput Math 4(4):389–396, 1995), constructed as polynomials on their compact support. They find a great amount of applications, in particular, in algorithms to construct complete Lyapunov functions. In this paper, we present a new code to construct Wendland functions of any order, as well as their derived auxiliary functions used for numerically solving PDEs. This new code simplifies the structure and the ease of use compared to the code presented in Argáez et al. (Wendland functions—a C++ code to compute them. In Proceedings of the 7th international conference on simulation and modelling methodologies, technologies and applications (2017), pp 323–330). Further, it optimises the routines to evaluate the functions and presents a new feature: a compilable LATE X report with all the instructions and steps to construct them.KeywordsWendland functionsC++Scientific computingApplied mathematicsInterpolating functionsCompactly supported functions
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