Rotating Detonation Engines (RDEs) appear promising for the demands of future propulsion. However, an issue of combustion instability needs to be given appropriate consideration in order to ensure trouble-free propulsion using the RDEs. Numerical simulations on a 2D RDE for the combustion of hydrogenoxygen are performed to examine the instabilities using the Dynamic Mode Decomposition (DMD) approach. A reactingFoam solver of OpenFOAM with Large Eddy Simulations (LES) and a PIMPLE solver with first-order temporal and second-order spatial schemes are used. Eddy Dissipation Model (EDM) is used to simulate turbulencecombustion interactions. The results are plotted in terms of line and contour plots of velocity, temperature, and pressure. A comparison of results with the reference data shows qualitative validation of the model. Single-point data might not provide the best knowledge of the instability. Therefore, the focus of the present work is to assess the feasibility of DMD to work with multi-point data for the identification of combustion instability. In the present work, it is shown that the DMD can be successfully used for the analysis of combustion instabilities that occur in RDEs.