Scholarlink

<p>One strategy to enhance the performance of the localized meshless radial basis function scheme in finite difference mode (RBF-FD) is to incorporate a polynomial term into the RBF-FD framework, known as the integrated radial basis function (IRBF) approach. In this work, we propose a comprehensive framework for obtaining the approximation weights for the IRBF method. Then, we derive analytical expressions for the weighting coefficients in the one-dimensional scenario for specific stencils, enabling us to explore the theoretical high-order convergence properties at the nodal points utilizing the Gaussian RBF. Furthermore, these weights are extended to be used for solving high-dimensional partial differential problems, such as the Poisson equation and the four-dimensional time-dependent Black-Scholes equation.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On convergence of integrated radial basis function approximations on specific stencils with numerical applications

  • 期刊论文

  • 发表日期：

    2025年5月23日

查看全文
  • Fazlollah Soleymani,
  • Shengfeng Zhu,
  • Mahdiar Barfeie

摘要

One strategy to enhance the performance of the localized meshless radial basis function scheme in finite difference mode (RBF-FD) is to incorporate a polynomial term into the RBF-FD framework, known as the integrated radial basis function (IRBF) approach. In this work, we propose a comprehensive framework for obtaining the approximation weights for the IRBF method. Then, we derive analytical expressions for the weighting coefficients in the one-dimensional scenario for specific stencils, enabling us to explore the theoretical high-order convergence properties at the nodal points utilizing the Gaussian RBF. Furthermore, these weights are extended to be used for solving high-dimensional partial differential problems, such as the Poisson equation and the four-dimensional time-dependent Black-Scholes equation.