Discreet Solutions for Matrix Systems in Partial Derivatives Hyperbolic and Singular

TL;DR

This paper develops a discrete method for solving strongly coupled hyperbolic partial differential systems using matrix separation, resulting in stable solutions through singular and Sturm-Liouville problems.

Contribution

It introduces a novel discrete separation approach for matrix PDE systems, combining singular and Sturm-Liouville problems for stability.

Findings

Successfully constructs stable discrete solutions

Decomposes complex systems into simpler difference equations

Provides a framework for solving coupled hyperbolic PDEs

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.