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<p>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.</p>

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Unisolvence of Randomized MultiQuadric Kansa Collocation for Convection–Diffusion with Mixed Boundary Conditions

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Maryam Mohammadi,
  • Alvise Sommariva,
  • Marco Vianello

摘要

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.