Native Julia Solvers for Ordinary Differential Equations Boundary Value Problem: A GSoC proposal

This is a proposal for the project "Native Julia solvers for ordinary differential equations and algebraic differential equations". There is no solver for ordinary differential equation (ODE) boundary value problem (BVP) yet in the JuliaDiffEq organization. I am going to implement native Julia solvers for ODE BVP problem. There are a number for advantages of Julia native solvers over calling C or Fortran's existing libraries via Julia's FFI, including the ability to use a wide variety of types in Julia like BigFloat for arbitrary precision, easier for people to contribute and better integrate with other packages in Julia ecosystem. The goals for this project are to implement BVP related data structures, a shooting method and a collocation method. Together, this contribution will help make Julia a viable environment for researchers and scientists to simulate models from boundary value problems.