%0 Journal Article %1 watson1979algorithm %A Watson, Layne T. %D 1979 %J SIAM Journal on Numerical Analysis %K 34b15-odes-nonlinear-bvps 65h20-global-methods-including-homotopy-approaches 65l10-numerical-analysis-odes-bvps %N 3 %R 10.1137/0716033 %T An Algorithm That is Globally Convergent with Probability One for a Class of Nonlinear Two-Point Boundary Value Problems %U https://epubs.siam.org/doi/abs/10.1137/0716033 %V 16 %X It is shown that the Chow–Yorke algorithm (a homotopy-type method) may be applied to a class of nonlinear two-point boundary value problems by solving the nonlinear system of equations defined by shooting. The resultant method is globally convergent with probability one, in the sense that it may fail for starting points in a set of Lebesgue measure zero. Some numerical results are given.

@article{watson1979algorithm, abstract = {It is shown that the Chow–Yorke algorithm (a homotopy-type method) may be applied to a class of nonlinear two-point boundary value problems by solving the nonlinear system of equations defined by shooting. The resultant method is globally convergent with probability one, in the sense that it may fail for starting points in a set of Lebesgue measure zero. Some numerical results are given.}, added-at = {2023-11-06T06:32:13.000+0100}, author = {Watson, Layne T.}, biburl = {https://www.bibsonomy.org/bibtex/266c0cac768a30091aa55be58a3c01c0f/gdmcbain}, doi = {10.1137/0716033}, interhash = {a04d6c8dc9b0592ec7e9972c547b5ab7}, intrahash = {66c0cac768a30091aa55be58a3c01c0f}, journal = {SIAM Journal on Numerical Analysis}, keywords = {34b15-odes-nonlinear-bvps 65h20-global-methods-including-homotopy-approaches 65l10-numerical-analysis-odes-bvps}, number = 3, timestamp = {2023-11-06T06:32:34.000+0100}, title = {An Algorithm That is Globally Convergent with Probability One for a Class of Nonlinear Two-Point Boundary Value Problems}, url = {https://epubs.siam.org/doi/abs/10.1137/0716033}, volume = 16, year = 1979 }