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The purpose of this research is to solve the Sturm-Liouville-type differential equation with Dirichlet boundary conditions. We employ a newly constructed locally supported wavelet basis based on Hermite \({\mathcal {C}}^1\) -quadratic splines over a regular grid. The new Hermite quadratic wavelet basis has been carefully adapted to the interval [0, 1] for improved computational simplicity. We validate our approach by presenting numerical examples at the end of this paper.

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Numerical Solution of Sturm-Liouville-Type Differential Equation Based on Wavelet Bases of Hermite Quadratic Splines

  • 会议论文

  • 发表日期：

    2025年

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  • Abdellah Lamnii,
  • Mohamed Lamnii,
  • Chaimae Mouhoub,
  • Driss Sbibih

摘要

The purpose of this research is to solve the Sturm-Liouville-type differential equation with Dirichlet boundary conditions. We employ a newly constructed locally supported wavelet basis based on Hermite \({\mathcal {C}}^1\) -quadratic splines over a regular grid. The new Hermite quadratic wavelet basis has been carefully adapted to the interval [0, 1] for improved computational simplicity. We validate our approach by presenting numerical examples at the end of this paper.