I specialize in Numerical Analysis as a computational mathematician, focusing on formulating numerical methods to address challenges in Biology and Physics. My past projects include utilizing Finite Differences to simulate biofilm growth. Lately, I've delved into Computational Fluid Dynamics, particularly working with the Navier-Stokes Equation. My current research centers around the non-linear Helmholtz equation, which describes electromagnetic wave behavior in Kerr media.  I currently conduct research on convergence, stability and error analysis of numerical schemes for partial differential equations.

• Efficiency and robustness of the (Anderson)-Picard-Newton Iteration for solving nonlinear PDES.

Jessica Franklin, Elizabeth Hawkins, Monica Morales-Hernandez, Leo G. Rebholz. (work in progress 2024)

• Stability of the Crank-Nicolson-Adams-Bashforth Scheme for the 2D Leray-Alpha Model

Authors:  Monica Morales Hernandez, Leo G. Rebholz, Cristina Tone, Florentina Tone. Numerical Methods for Partial Differential Equations Vol.  32, 4, Pages 1155–1183. 29 December 2015.

• A note on helicity conservation in Leray models of incompressible flow

Authors:  Monica Morales Hernandez, Leo G. Rebholz. Journal of Mathematical Analysis and Applications. Volume 422, Issue 1, Pages 776-781. 1 February 2015.

• Corrigendum:  An  efficient  recursive  algorithm  in  the  computational  modeling  of  the bounded growth of biological films.

Authors:  Monica Morales Hernandez, J.E. Macias-Diaz et.al. International Journal of Computational Methods. Vol.  10, No.  1 1392001 [4 pages] 28 February 2013

• An efficient recursive algorithm in the computational modeling of the bounded growth of biological films.

Authors:  Monica Morales Hernandez, J.E. Macias-Diaz et.al. International Journal of Computational Methods. Vol.  09, No.  4 1250050 [15 pages] 14 December 2012