Artículos FC IFIS

Permanent URI for this collection

https://repositoriovip.uasd.edu.do/handle/123456789/104

Browse

Browsing Artículos FC IFIS by Author "Juan R. Holguín"

Now showing 1 - 1 of 1
  • Item
    A Jacobi–spectral framework for the heat equation with Dirichlet boundary conditions
    (2026-03-09) Juan Toribio Milane; José A. Gómez Hernández; Juan R. Holguín; Pedro N. Tifa de Jesús
    We developed a Jacobi–spectral framework for the heat equation in a spherical domain under axial symmetry and Dirichlet boundary conditions. The angular part of the Laplacian was realized as a Jacobi Sturm–Liouville operator on a weighted space, enabling the Jacobi transform to diagonalize the angular component and project the partial diferential equation (PDE) onto a sequence of decoupled radial problems. Each projected equation reduced to a Euler-type radial ordinary diferential equation (ODE) driven by the corresponding Jacobi coefficient of the source term. These modal equations were solved in terms of spherical-Bessel eigenfunctions and radial Green kernels, yielding explicit Duhamel-type formulas for the time-dependent coefficients and establishing convergence in the weighted space. The Legendre case recovered the classical axisymmetric model, while general Jacobi parameters provided a unified extension of this setting. A central result was the demonstration of a rigorous equivalence between the Jacobi–spectral representation and the classical separation-of-variables solution written in spherical harmonics and spherical-Bessel modes. The proposed framework clarified the angular–radial coupling in spherical geometries and connected naturally with modern Jacobi and ultraspherical spectral methods.