The Journal of the Indian Mathematical Society

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Uniqueness and the Convergence of Successive Approximations


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1 Massachusetts Institute of Technology, Cambridge 39, Mass, United States
     

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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.
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  • Uniqueness and the Convergence of Successive Approximations

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Authors

E. A. Coddington
Massachusetts Institute of Technology, Cambridge 39, Mass, United States
N. Levinson
Massachusetts Institute of Technology, Cambridge 39, Mass, United States

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.