2025-07-24 –, Main Room 3
Boundary value problems arise in various scientific domains and play an important role in scientific computing, how to efficiently solve them is vital in numerical simulations. BoundaryValueDiffEq.jl as a crucial part of DifferentialEquations.jl provides powerful BVP solvers and tackles various kinds of BVP problems. In this talk, the presenter will talk about the latest development of BoundaryValueDiffEq.jl and why it makes itself a powerful and robust package.
Boundary value problems (BVPs) represent a critical and expansive class of differential equations that arise in various scientific fields, such as physics, economics, and many more. These problems typically involve finding a solution to a differential equation subject to certain specified values in some points among interval, known as boundary conditions. The efficiency and precision in solving these problems are important due to their widespread applications, ranging from modeling physical phenomena to optimizing engineering systems.
BoundaryValueDiffEq.jl is part of the DifferentialEquations.jl ecosystem, known for its comprehensive suite of tools for solving differential equations. This package has been enriched with several state-of-the-art features, making it a powerful and robust solver for a variety of BVPs. BoundaryValueDiffEq.jl offers a bunch of fast solvers including fully-implicit solvers, Nystrom solvers, etc, and integrates several advanced features such as error control adaptivity, tailored sparse AD, etc. In this talk, we will explore the latest advancements in BoundaryValueDiffEq.jl, which have significantly enhanced the capabilities for solving boundary value problems.
In summary, the ongoing development in BoundaryValueDiffEq.jl has transformed it into a versatile and robust tool for solving a wide array of boundary value problems with enhanced efficiency and precision. This talk will delve into the technical details of these new features, demonstrate their application through practical examples, and highlight the future directions of research and development in this vital area of scientific computing.
I am a master's student in machine learning and industrial control systems at Zhejiang University. My research interest focuses on the intersection of machine learning and dynamical systems. I participated in GSoC 2023 with SciML under the NUMFOCUS umbrella.