Diferencias finitas

This research area focuses on developing numerical schemes of arbitrary high order accuracy for nonlinear systems governed by conservation laws. Traditional Lax-Wendroff methods face challenges when extended to nonlinear problems due to the complexity of transforming temporal derivatives into spatial ones (via Cauchy-Kovalevsky procedures). New approaches approximate temporal derivatives or adaptively adjust the methods locally to maintain high-order accuracy while addressing stability issues near discontinuities. This theme matters because solving nonlinear conservation laws accurately and efficiently is critical in computational fluid dynamics, physics, and engineering applications involving shocks and complex wave interactions.

This thematic area addresses the challenges of solving parabolic partial differential equations (especially heat/diffusion equations) under uncertain input parameters and boundary/initial conditions. Recognizing the intrinsic variability and measurement errors in physical problems, researchers develop hybrid numerical-stochastic methods, combining finite difference discretizations with uncertainty quantification techniques (e.g., Monte Carlo simulations). This line of research is vital for producing reliable and robust predictions in engineering, physics, and environmental sciences where data uncertainty critically affects solution accuracy and decision-making.

This theme investigates the structural effects caused by the expansion of financial markets and fiscal policy instruments such as intergovernmental transfers. Topics include the conceptualization and consequences of financialization, inequities generated by fiscal allocations and subsidies, and their influence on labor markets, public sector wages, and regional economic disparities. Understanding these dynamics is important for informing equitable fiscal policy design and mitigating the adverse social impacts of financial system transformations.