I look for a numerical method to solve boundary value problems for systems of differential and algebraic equations of the form F(x,y,y') = 0, G(x,y) = 0, y(a) = ya, y(b) = yb, where y = (y1, y2, ... yn). I have to implement it myself, but I can't find such methods in textbooks. Where can I find description of needed method?
Methods for solving BVP for DAE
numerical analysis
The main methods I'm aware of are collocation methods. The best source I can think of on the topic is Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by Ascher, Mattheij, and Russell, in which they devote a chapter to methods applicable to DAEs and generalized ODEs. One package for solving BVPs for DAE is COLDAE by Ascher and Spiteri; relevant references for the methods implemented therein can be found in the comment block at the start of the file in the link.Differential-Algebraic Equations: Analysis and Numerical Solution by Kunkel and Mehrmann is a more up-to-date reference. I've only skimmed the book; a former colleague of mine recommended it.