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?
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$\begingroup$ You may want to check the answers here for methods and references. However, because of the DAEs involved, your question needs a separate answer. $\endgroup$– JanCommented Feb 7, 2014 at 8:44
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$\begingroup$ Thank you for the answer. I know a method for solving BVPs for ODEs. In my problems some y's may be eliminated from G(x, y) = 0 numerically with Newton's method, and the problems may be reduced to ordinary BVPs for ODEs, but this seems to be cumbersome method. So I'm interested in some other method. $\endgroup$– XDRMCommented Feb 7, 2014 at 10:45
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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.
answered Feb 7, 2014 at 13:47