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

**URL:** <https://discourse.julialang.org/t/sciml-numfocus-small-development-grant-collocation-methods-for-boundary-value-differential-algebraic-equations/113329>\
**Category:** Community\
**Tags:** diffeq, grants\
**Created:** [April 22, 2024, 11:08am UTC](https://discourse.julialang.org/t/sciml-numfocus-small-development-grant-collocation-methods-for-boundary-value-differential-algebraic-equations/113329 "2024-04-22T11:08:03Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [April 22, 2024, 11:08am UTC](https://discourse.julialang.org/t/sciml-numfocus-small-development-grant-collocation-methods-for-boundary-value-differential-algebraic-equations/113329/1 "2024-04-22T11:08:03Z")

</div>

I am happy to announce the latest funded project in SciML: Collocation Methods for Boundary Value Differential-Algebraic Equations. This is highly requested functionality and thus I am happy to announce our plans to build new solvers over the summer!

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](https://github.com/SciML/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](https://docs.sciml.ai/SciMLBenchmarksOutput/stable/), it is still not adequate for some complex scenarios involving differential-algebraic equations. Though SciML offers [powerful solvers](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/dae_example/) 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.

This should have lots of applications especially in optimal control.

For more information see:

> **[SciML: Open Source Software for Scientific Machine Learning](https://sciml.ai/news/2024/04/16/numfocus_sdg/)**
>
> Open Source Software for Scientific Machine Learning