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Wavelet Collocation Method Based on Biorthogonal Flatlet Multiwavelet and Its Application in Solving the Singular BVPs

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  • Maryam Mohseni
  • Davood Rostamy

Abstract

The main focus of our work is to provide a computationally efficient approximate algorithm for finding a numerical solution of singular boundary value problems (SBVPs). For this purpose, we apply a biorthogonal flatlet multiwavelet collocation method (BFMCM) to solve numerically. This is performed by approximating functions using a BFMCM. In addition, the implementation of the introduced method, convergence analysis, and numerical stability are presented. To verify the efficiency and usefulness of the proposed method, several examples are presented, and to compare the obtained numerical results with the exact solutions as well as with other numerical approaches, some numerical tables and absolute error diagrams are drawn for all problems. The main advantage of this method is its efficiency and accuracy even when using a small number of basis functions, as well as its ease of implementation.

Suggested Citation

  • Maryam Mohseni & Davood Rostamy, 2026. "Wavelet Collocation Method Based on Biorthogonal Flatlet Multiwavelet and Its Application in Solving the Singular BVPs," International Journal of Differential Equations, Hindawi, vol. 2026, pages 1-17, September.
    • Handle: RePEc:hin:jnijde:3205012
    DOI: 10.1155/ijde/3205012
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