A Closed-Form Solution to the Arbitrary Order Cauchy Problem with Propagators

TL;DR

This paper presents a closed-form solution for arbitrary order Cauchy problems using exponential propagators, simplifying the solution process through a novel series and differential equation approach.

Contribution

It introduces a new closed-form solution for arbitrary order Cauchy problems utilizing exponential propagators and a homogeneous differential equation.

Findings

Closed-form solution for arbitrary order Cauchy problems.

Representation as a sum of exponential propagator functions.

Simplified solution derivation using a homogeneous differential equation.

Abstract

The general abstract arbitrary order (N) Cauchy problem was solved in a closed form as a sum of exponential propagator functions. The infinite sparse exponential series was solved with the aid of a homogeneous differential equation. It generated a linear combination of exponential functions. The Cauchy problem solution was formed with N linear combinations of N exponential propagators.