Uniqueness and the Convergence of Successive Approximations

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Authors

  • Massachusetts Institute of Technology, Cambridge 39, Mass ,US
  • Massachusetts Institute of Technology, Cambridge 39, Mass ,US

DOI:

https://doi.org/10.18311/jims/1952/17050

Abstract

Although the uniqueness of the solution of an initial value problem of ordinary differential equations does not imply the convergence of the successive approximations (cf. the example due to Muller, [4] ), it is known that many of the sufficient conditions for uniqueness, with a certain requirement of monotonicity, do imply the convergence of these approximations to the solution.