In this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the theory of the presented method is justified by proving the corresponding convergence result. Likewise, to illustrate this method, some graphical and numerical examples are presented in ${\mathbb{R}}^2$, and a comparison with another work is analyzed.

In this paper we propose an approximation method for solving second kind Volterra integral equation systems by radial basis functions. It is based on the minimization of a suitable functional in a discrete space generated by compactly supported radial basis functions of Wendland type. We prove two convergence results, and we highlight this because most recent published papers in the literature do not include any. We present some numerical examples in order to show and justify the validity of the proposed method. Our proposed technique gives an acceptable accuracy with small use of the data, resulting also in a low computational cost.