A comparison between the Shooting and Finite-Difference Method in solving a Nonlinear Boundary Value Problem found in the context of light propagation

TL;DR

This paper compares the shooting and finite-difference methods for solving a nonlinear boundary value problem related to light propagation, finding that finite-difference is more stable and converges faster.

Contribution

The paper provides a comparative analysis of shooting and finite-difference methods implemented in Matlab for a specific nonlinear BVP in light propagation.

Findings

Finite-difference method is more numerically stable.

Finite-difference converges faster than shooting.

Finite-difference outperforms shooting in this context.

Abstract

The shooting and finite-difference method are both numeric methods that approximate the solution of a BVP to a given accuracy. In this report both methods were implemented in Matlab and compared to each other on a BVP found in the context of light propagation in nonlinear dielectrics. It was observed that the finite-difference method is numerically more stable and converges faster than the shooting method.