Solving General Equations by Order Completion

TL;DR

This paper introduces an order completion method for solving a wide range of equations, including complex nonlinear PDE systems with initial and boundary conditions, offering a new approach to these challenging problems.

Contribution

It presents a novel order completion technique that extends the solvability of general equations, especially nonlinear PDEs, beyond traditional methods.

Findings

Applicable to large classes of nonlinear PDEs

Handles initial and boundary value problems effectively

Provides a new framework for solving complex equations

Abstract

A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.