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A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

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  • Watanabe, Yoshitaka
  • Nakao, Mitsuhiro T.

Abstract

This paper describes a numerical verification of solutions for infinite-dimensional functional equations based on residual forms and Newton-like iteration. The method is based upon a verification method previously developed by the authors. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations, are presented.

Suggested Citation

  • Watanabe, Yoshitaka & Nakao, Mitsuhiro T., 2016. "A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 239-251.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:239-251
    DOI: 10.1016/j.amc.2015.12.021
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    1. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(5), pages 687-698, October.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    4. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(3), pages 381-386, June.
    5. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(4), pages 525-537, August.
    6. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(2), pages 285-292, April.
    7. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 151-159, February.
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