arXiv subjects

Filomena Di Tommaso

Publications and source records attributed to Filomena Di Tommaso.

3 recordsLinked to original sources

arXiv2025

Multinode Shepard Functions and Tensor Product Polynomial Interpolation: Applications to Digital Elevation Models

The paper presents an in-depth exploration of the multinode Shepard interpolant on a regular rectangular grid, demonstrating its efficacy in reconstructing surfaces from DEM data. Additionally, we study the approximation order associated to this interpolant and present a detailed algorithm for reconstructing surfaces. Numerical tests showcase the effectiveness of the proposed algorithm.

math.NA↗

arXiv2025

Multinode Shepard collocation method for pricing of financial derivatives

This paper explores the use of the multinode Shepard method for the numerical solution of the two-dimensional Black-Scholes equation. The proposed approach integrates a spatial approximation via the multinode Shepard operator with a temporal discretization based on the Backward Difference Formula. Numerical experiments are presented to demonstrate the accuracy and effectiveness of the method.

math.NA↗

arXiv2025

The univariate multinode Shepard method for the Caputo fractional derivatives: from Approximation to the solution of Bagley-Torvik equation

In this paper, we approximate the fractional derivative of a given function using the univariate multinode Shepard method through the Gauss-Jacobi quadrature formula. Subsequently, the proposed method is applied to the numerical solution of boundary value problems (BVPs) and initial value problems (IVPs), specifically addressing the Bagley-Torvik equations. Experimental results confirm the method's effectiveness, particularly in accurately approximating the Bagley-Torvik equation for both BVPs and IVPs.

math.NA↗