ICIAM2023 Springer Series – serie

This open access book highlights the critical role of numerical software libraries in advancing applied mathematics and enabling faster, more accurate simulations in science and engineering. These libraries provide high-quality implementations of efficient algorithms, facilitating the transfer of new mathematical methods into practical applications across laboratory and industrial settings. Their importance has grown significantly in recent years, as demonstrated by the U.S. Department of Energy’s Exascale Computing Project (ECP), where libraries have helped applications adapt to cutting-edge exascale systems while improving performance on traditional architectures. The impact of these developments was underscored during the 2023 International Congress on Industrial and Applied Mathematics through a three-part minisymposium titled “Numerical Software Libraries Enabling Benefits to Scientific Applications.” These sessions showcased efforts to maximize the value of libraries, presenting examples of new algorithms and performance enhancements across diverse application areas. This volume compiles chapters based on examples presented during these sessions that illustrate the profound impact of applied mathematics on modern computational science and engineering via modern numerical software libraries.

mso-fareast-font-family: 'Times New Roman';">This book presents a collection of research papers exploring innovative applications of Artificial Intelligence (AI) in Industrial and Applied Mathematics (IAM). Another contribution discusses eXplainable AI (XAI), highlighting how Clifford geometric algebra can enhance AI interpretability.

mso-fareast-language: EN-US;">This book presents a collection of recent advances in stochastic numerical analysis and computational finance. The volume highlights cutting-edge developments in numerical techniques for stochastic differential equations and stochastic models in finance.

mso-themeshade: 128;">This open access book contains review/research papers authored by fourteen plenary/invited speakers to the 10th International Congress on Industrial and Applied Mathematics (Tokyo, August 20–25, 2023).

This book presents the proceedings of two minisymposia—“Delay and Stochastic Differential Equations in Life Sciences and Engineering” and “Stochastic Modelling in Finance”—held at the International Congress on Industrial and Applied Mathematics (ICIAM) 2023 in Tokyo, Japan. It brings together a diverse collection of theoretical and applied research in delay and stochastic differential equations (DDEs and SDEs), showcasing the depth and breadth of current developments in these areas.The papers included in this book reflect the high quality and versatility of research presented at the sessions. Covering a wide range of topics, they collectively illustrate the richness of delay and stochasticity as drivers of complex dynamical behavior. Each contribution has undergone a rigorous peer-review process to ensure the highest standards of publication.Key topics include delay and resonance, periodic solutions, numerical methods for SDEs, Cesàro limits for Volterra convolution equations, stochastic modeling and big data in finance, incomplete market analysis, deterministic and stochastic pantograph equations. This book aims to provide readers with a cohesive and insightful overview of current research in DDEs and SDEs, while inspiring future innovations and applications across disciplines—from physics and biology to financial engineering.

This book brings together groundbreaking research papers authored by distinguished experts and scholars. Each contribution delves into innovative aspects of splitting optimization—ranging from theoretical advancements and methodological developments to a diverse array of applications. The book offers readers a comprehensive and cohesive overview of the current state of splitting optimization, while inspiring continued research and innovation in this dynamic field.

This book presents a curated collection of recent research contributions in the field of nonlinear partial differential equations (PDEs), with an emphasis on hyperbolic problems. These equations are essential for modeling  complex physical phenomena such as wave propagation, fluid dynamics, blood flow, and sediment transport. In many real-world applications, the governing equations are not purely hyperbolic but involve intricate interactions with elliptic or parabolic components.As the field advances through theoretical insights and practical needs, this volume captures innovative developments shaping current research. The contributions included here were originally presented at the 10th International Congress on Industrial and Applied Mathematics (ICIAM), held in Tokyo in 2023. They were selected from minisymposia on hyperbolic PDEs and related topics, each organized by leading experts in the field.The chapters in this book reflect a rich diversity of perspectives and approaches, ranging from rigorous mathematical analysis to computational techniques and real-world applications. By bringing together these works, the volume offers a comprehensive snapshot of the state of the art in hyperbolic PDE research, highlighting both foundational insights and emerging trends.Edited by the organizers of the relevant ICIAM 2023 minisymposia, this book serves as a valuable resource for researchers, practitioners, and graduate students interested in the theoretical and applied aspects of nonlinear PDEs. Whether you are exploring the mathematical underpinnings of wave phenomena or developing models for complex systems in science and engineering, this volume provides both inspiration and practical tools to advance your work.

This book presents a compelling and up-to-date exploration of modeling techniques for digital twins, a transformative concept revolutionizing how physical assets are designed, operated, optimized, and managed throughout their lifecycle. Digital twins are precise virtual counterparts of physical systems, capable of integrating real-time data to offer dynamic, predictive insights into system behavior. As this paradigm gains momentum across industries, it enhances decision-making and operational efficiency but also introduces new mathematical and engineering challenges in model development.At the core of this volume is a thorough investigation into the modeling frameworks essential for building effective digital twins. These systems must fulfill multifunctional roles, requiring models that are both robust and flexible enough to simulate complex physical processes with high fidelity. The book spans a wide spectrum of approaches from physics-based models grounded in the laws of nature to data-driven techniques that harness large-scale datasets. It also highlights the growing importance of hybrid methods that combine the interpretability of physical models with the adaptability of machine learning. Throughout the book, real-world case studies illustrate how these modeling advancements are applied to solve pressing challenges in sectors such as manufacturing, energy and transportation.This volume brings together contributions from leading researchers who are shaping the future of digital twins. The chapters are designed to be accessible to a broad audience. Whether you just started or want to deepen your expertise, this volume offers the insights and tools needed to engage with one of the most exciting developments in modern applied mathematics and engineering.

This book presents the proceedings of the Minisymposium “Various Methods for the Analysis of PDEs” held at the International Congress on Industrial and Applied Mathematics (ICIAM) 2023. This volume brings together a diverse group of researchers, practitioners, and experts who have shared their latest developments and innovations in the field of Partial Differential Equations (PDEs).The papers included in this volume reflect the high quality and breadth of research presented at the session. Covering a wide range of topics, this collection showcases the dynamic and interdisciplinary nature of the Analysis of PDEs. Each contribution has undergone a rigorous peer-review process to ensure the highest standards of academic excellence.Key topics include:Interpolation Inequalities: Novel contributions to the field, including stability results for the Sobolev inequality and the Gaussian logarithmic Sobolev inequality with explicit and dimensionally sharp constants.Strichartz Estimates: New estimates specifically for orthonormal families of initial data, extending traditional Strichartz estimates to provide deeper insights into the behavior of solutions to dispersive equations, including the wave equation, Klein-Gordon equation, and fractional Schrödinger equations.Asymptotic Behavior: Detailed analysis of the asymptotic behavior for the massive Maxwell–Klein–Gordon system under the Lorenz gauge condition in dimension (1+4), including scattering results.Time-Dependent Free Schrödinger Operator: A new characterization of this operator, highlighting its unique invariance under the Galilei group in Euclidean space-time.Lifespan Estimates: Analysis of the lifespan of solutions to the damped wave equation, with decay estimates for particular initial data in the case of nonlinearity with subcritical Fujita exponent.This book aims to provide readers with a profound and cohesive understanding of the current state of splitting optimization while inspiring future research and innovation in this dynamic field.