Unisolvence of randomized MultiQuadric Kansa collocation for convection-diffusion with mixed boundary conditions
Numerical Analysis
2025-03-04 v1 Numerical Analysis
Abstract
We make a further step in the open problem of unisolvence for unsymmetric Kansa collocation, proving that the MultiQuadric Kansa method with fixed collocation points and random fictitious centers is almost surely unisolvent, for stationary convection-diffusion equations with mixed boundary conditions on general domains. For the purpose of illustration, the method is applied in 2D with fictitious centers that are local random perturbations of predetermined collocation points.
Cite
@article{arxiv.2503.00963,
title = {Unisolvence of randomized MultiQuadric Kansa collocation for convection-diffusion with mixed boundary conditions},
author = {Maryam Mohammadi and Alvise Sommariva and Marco Vianello},
journal= {arXiv preprint arXiv:2503.00963},
year = {2025}
}