Numerical methods for complex differential equation models
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Yu Feng
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Great Bay University
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Peoples Rep of China
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Liu Liu
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Chinese University of Hong Kong
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Hong Kong
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Yanli Wang
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Beijing Computational Science Research Center
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Peoples Rep of China
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Introduction:
| | Differential equation models play a fundamental role in describing complex phenomena in the natural sciences, engineering, and socio-economic systems. These models are often characterized by strong nonlinearities, multiscale interactions, high dimensionality, and limited or noisy data, which pose significant challenges for numerical computation.
This session focuses on recent advances in numerical methods for complex differential equation models, with an emphasis on robust, efficient, and reliable computational techniques. Topics include classical numerical methods for ordinary and partial differential equations, such as finite difference, finite element, and time integration methods, as well as modern approaches for stiff, multiscale, and high-dimensional systems.
The session also welcomes contributions on hybrid and data-assisted numerical methods, including physics-informed and structure-aware machine learning approaches, which aim to enhance traditional numerical frameworks while respecting underlying mathematical and physical constraints. Particular attention will be paid to stability, accuracy, and structure preservation in challenging modeling settings.
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