This book gathers selected contributions from invited speakers at Tudela Numérica 2024, a school and research meeting devoted to numerical analysis and computational mathematics, held at the Public University of Navarre.

The chapters reflect current research directions in model reduction, high-performance computing, and numerical methods for partial differential equations. They include advances in the iterative computation of intrinsic proper generalized decomposition (PGD) modes for symmetric elliptic parametric problems, providing efficient reduced representations for complex systems. Efficient implicit solvers for large-scale models of neural networks address stability and scalability challenges arising in computational neuroscience.

Specific contributions examine first-order parareal splitting methods for the space-time parallel solution of parabolic problems and multigrid methods on logically rectangular meshes, from both intrusive and non-intrusive perspectives. Practical aspects of scientific computing are also represented through an introduction to geometry description and mesh generation using Gmsh within finite element implementations.

 Altogether,this book highlights the interplay among mathematical analysis, algorithm design, and computational practice that defines modern numerical analysis.

Macarena Gómez-Mármol is Full Professor of mathematical analysis at Universidad de Sevilla, specializing in numerical analysis and differential equations, with applications to fluid dynamics and model reduction.

María Luisa Rapún is a Full Professor of applied mathematics at Universidad Politécnica de Madrid. Her research focuses on numerical methods, boundary element techniques, and inverse and defect detection problems, with strong links to industrial applications.

Víctor Domínguez is Associate Professor of applied mathematics at Universidad Pública de Navarra, whose work focuses on numerical analysis and computational mathematics, particularly boundary and finite element methods.

Laura Portero is  Associate Professor of applied mathematics at Universidad Pública de Navarra, working on numerical methods and finite element analysis, including research on mixed formulations.

Andrés Arrarás is  Associate Professor of applied mathematics at Universidad Pública de Navarra. His research addresses numerical schemes and discretization techniques for partial differential equations and applications.