Soluciones Discretas para Sistemas Matriciales en Derivadas Parciales Hiperbolicos y Singulares

TL;DR

This paper develops a discrete method for solving strongly coupled hyperbolic partial differential systems, using matrix separation and superposition to ensure stability and handle singularities.

Contribution

It introduces a novel discrete separation of variables approach for hyperbolic matrix PDEs, including singular and Sturm-Liouville problems, ensuring stable solutions.

Findings

Successfully constructs stable discrete solutions for coupled hyperbolic PDEs.

Derives separate difference equations for singular and Sturm-Liouville problems.

Demonstrates the method's effectiveness in handling singularities and coupling.

Abstract

In this paper we study the construction of a discrete solution for a hyperbolic system of partial differentials of the strongly coupled type. In its construction, the discrete separation of matricial variable method was followed. Two separate equations in differences were obtained: a singular matricial and the other one a Sturm Liouville vectorial problem, which by the superposition principle yield a stable discrete solution.