# Numerical solutions to an inverse problem for a non-linear Helmholtz equation

## DOI:

https://doi.org/10.21914/anziamj.v64.17954## Abstract

In this work, we develop numerical methods to solve forward and inverse wave problems for a nonlinear Helmholtz equation defined in a spherical shell between two concentric spheres centred at the origin. A spectral method is developed to solve the forward problem while a combination of a finite difference approximation and the least squares method are derived for the inverse problem. Numerical examples are given to verify the method.

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## Published

2023-10-28

## Issue

## Section

Proceedings Computational Techniques and Applications Conference