NumFOCUS small development grant: Collocation Methods for Boundary Value Differential-Algebraic Equations

The SciML organization is pleased to announce that we have received a small development grant from NumFOCUS to integrate Collocation Methods for Boundary Value Differential-Algebraic Equations to DifferentialEquations.jl.

At present, for boundary value problems, there are Mono-Implicit Runge-Kutta(MIRK) methods and Shooting methods for first-order BVPs, MIRKN methods for second-order BVPs in BoundaryValueDiffEq.jl. While these solvers can cover many common boundary value problems and outperform some famous Fortran BVP solvers such as BVPSOL, BVPSOLVER and COLNEW in benchmarks, it is still not adequate for some complex scenarios involving differential-algebraic equations. Though SciML offers powerful solvers for systems of DAEs solving, there are no robust solvers for boundary value DAEs even in well-built tools like MATLAB or Mathematica. With this grant, SciML will deliver powerful BVDAE solvers to address the current problems and provide a more comprehensive solution for complex numerical simulations.

The grant would have two important deliverables:

  1. Efficient boundary value differential-algebraic equations solvers for nonlinear systems of semi-explicit DAEs of index at most 2.

  2. Thorough benchmarks and documentation, demonstrate the performance and robustness of the new solvers.

The person being funded is Qingyu Qu, an active contributor to SciML with a focus on numerical methods for differential equations and machine learning.

Qingyu will be working on a part-time basis throughout the upcoming year and will present an update at JuliaCon 2024.