How does BVP5C algorithm linearize nonlinear algebraic equations?

2021 10 11
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My understanding is that BVP5C forms set of generally nonlinear algebraic equation in each collocation interval, linearizes them, and iteratively solves with linear equation solvers of MATLAB. How is Linearization done? I could not find the answer in the following papers:
1. Shampine LF, Kierzenka J, Reichelt MW. Solving Boundary Value Problems for Ordinary Differential Equations in Matlab with bvp4c. :27.
2. Kierzenka J, Shampine LF. A BVP Solver that Controls Residual and Error. 2008;16.

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