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Explore asymptotic-preserving numerical schemes for solving multiscale physical problems in this comprehensive lecture delivered at the International Conference on Biological Sciences 2025. Learn how these specialized computational methods maintain accuracy across multiple scales of physical phenomena, from microscopic to macroscopic regimes, while preserving the asymptotic behavior of the underlying mathematical models. Discover the theoretical foundations, implementation strategies, and practical applications of asymptotic-preserving schemes in various fields of physics and applied mathematics. Gain insights into how these numerical techniques handle the computational challenges that arise when dealing with problems involving vastly different time and length scales, making them essential tools for modern scientific computing and mathematical modeling.
