F.: Effects of partial magnetic field in a vented square cavity with aiding and opposing of MWCNT-water nanofluid flows (2021) Poggiali, D.: Multivariate approximation at fake nodes (2021) Cavoretto, Roberto: Adaptive radial basis function partition of unity interpolation: a bivariate algorithm for unstructured data (2021).D.: On the search of the shape parameter in radial basis functions using univariate global optimization methods (2021) Perracchione, E.: Learning via variably scaled kernels (2021) Campagna, Rosanna Perracchione, Emma: Data-driven extrapolation via feature augmentation based on variably scaled thin plate splines (2021).

Zheng, Hui Fan, Zhuowan Li, Jichun: Simulation of electromagnetic wave propagations in negative index materials by the localized RBF-collocation method (2022).Santin, Gabriele Karvonen, Toni Haasdonk, Bernard: Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces (2022).Massei, Stefano: Some algorithms for maximum volume and cross approximation of symmetric semidefinite matrices (2022).The new meshfree methods not only avoid the complexity of mesh generation, but also solve the radiation diffusion problem with high accuracy. In the end, the accuracy and efficiency of the presented algorithms are verified by 1D and 2D numerical experiments. Second, the successive permutation iterative algorithms for full-implicit discretization on time are constructed furtherly, which are more efficient than the former algorithm. At first, the part of diffusion terms for 1D and 2D radiation diffusion equations are linearized directly on time to form the new implicit schemes, and Kansa’s non-symmetric collocation method with the compactly supported radial basis function is used to solve the radiation diffusion problem. In the paper, we will provide a kind of new fast meshfree methods based on radial basis functions. Since it is modeled by nonlinear equations that are usually solved in complex domains, it is difficult to solve by means of finite element method and finite difference method and so on. Radiation diffusion is a phenomenon of interest in the field of astrophysics, inertial confinement fusion and so on.

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