A computational algebraic approach for the study of polynomial sequences. Examples and applications

Author : Anna Napoli

Abstract :In this work, we aim to outline a path for studying polynomial sequences using a computational algebraic approach. We consider the particular case of Appell polynomials. A key application of this approach is umbral interpolation, where a linear functional and a operator are used to construct interpolating polynomials. By applying umbral interpolation, we derive ecient numerical integration methods. Finally, we address the umbral dierential problem: we obtain methods for the numerical solution of higher order non linear ordinary dierential equations associated with general umbral interpolating conditions.

Keywords :Appell polynomials, umbral interpolation, computational algebra, ODEs, integration

Conference Name :International Conference on Pure and Applied Mathematics (ICPAM-25)

Conference Place Prague, Europe

Conference Date 25th Jul 2025