# Increasing stability of the inverse source problem for one dimensional domain

## TL;DR

This paper demonstrates that using multi-frequency waves at the endpoints of a one-dimensional domain enhances the stability of the inverse source problem for the Helmholtz equation, balancing data discrepancy and high-frequency effects.

## Contribution

The paper introduces a stability estimate for the inverse source problem that incorporates multi-frequency data at domain endpoints, improving stability analysis.

## Key findings

- Stability improves with multi-frequency data at endpoints.
- The stability estimate accounts for data discrepancy and high-frequency tail.
- Multi-frequency approach enhances inverse problem robustness.

## Abstract

Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end points. Our main result is a stability estimate consists of two parts: the data discrepancy and the high frequency tail.