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<p>This work presents a rigorous analysis of a cubic orthogonal spline collocation (OSC) method for a two-dimensional nonlinear-nonlocal Euler-Bernoulli plate model. The proposed scheme combines the OSC method with a three-point central difference discretization to approximate the coupled system of partial differential equations. The nonlinear-nonlocal damping term is evaluated accurately using the Gauss-Legendre quadrature rule. A comprehensive stability analysis is conducted, and optimal convergence estimates are established for the fully discrete OSC formulation. The theoretical results are supported by several numerical experiments, which confirm the accuracy and efficiency of the proposed approach.</p>

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Cubic orthogonal spline collocation method for Euler-Bernoulli plates with the nonlinear-nonlocal damping

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Kexin Li,
  • Tao Guo,
  • Wenlin Qiu,
  • Mengmeng Liu

摘要

This work presents a rigorous analysis of a cubic orthogonal spline collocation (OSC) method for a two-dimensional nonlinear-nonlocal Euler-Bernoulli plate model. The proposed scheme combines the OSC method with a three-point central difference discretization to approximate the coupled system of partial differential equations. The nonlinear-nonlocal damping term is evaluated accurately using the Gauss-Legendre quadrature rule. A comprehensive stability analysis is conducted, and optimal convergence estimates are established for the fully discrete OSC formulation. The theoretical results are supported by several numerical experiments, which confirm the accuracy and efficiency of the proposed approach.