Bin Wang Knihy

Focusing on recent advancements, this book delves into structure-preserving algorithms tailored for oscillatory differential equations, relevant across fields like astronomy and quantum mechanics. It systematically reviews innovative integrators, including exponential and energy-preserving methods, alongside time-stepping techniques. Theoretical analyses highlight the benefits of these new approaches, demonstrating their effectiveness over traditional methods. Additionally, it tackles contemporary challenges in numerical analysis, offering a comprehensive array of modern tools and techniques.

Focusing on geometric numerical integration, this monograph delves into structure-preserving algorithms that emerged in the 1980s, emphasizing their role in identifying long-term behaviors and conservation laws in dynamic systems. It addresses the challenges posed by highly oscillatory problems, which involve periodic or quasiperiodic solutions across extensive time intervals. The work highlights the necessity for innovative geometric integrators tailored for both ordinary and partial differential equations, reflecting the growing significance of this area in contemporary mathematical research.

More than half of the world’s people inhabit the region of the Asian monsoon—a region where torrential rains, floods, storms, cold-air surges, droughts, and heat waves are a part of the economy, culture, and rhythms of life. Showing the strongest seasonal variations in the Earth’s climate system, the Asian monsoon has far-reaching impacts on global climate and the environment. Its variability exemplifies complex interactions among the Earth’s surface, ocean, atmosphere, and biosphere. Prediction of monsoon climate fluctuation and future change is one of the greatest scientific challenges and deepest societal concerns.