Numerical existence theorem for solutions of two-point boundary value problems of nonlinear differential equations

@article{Takayasu2010NumericalET,
  title={Numerical existence theorem for solutions of two-point boundary value problems of nonlinear differential equations},
  author={Akitoshi Takayasu and Shin'ichi Oishi and Takayuki Kubo},
  journal={Nonlinear Theory and Its Applications, IEICE},
  year={2010},
  volume={1},
  pages={105-118}
}
In this paper, a numerical method is presented for verifying the existence and uniqueness of solutions to two-point boundary value problems of nonlinear ordinary differential equations. Taking into account every error of numerical computations such as the discretization error and the rounding error, this method also provides mathematically guaranteed error bounds between approximations obtained by numerical computations and the exact solution whose existence is proven by the numerical existence… 

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