The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Uniqueness and the Convergence of Successive Approximations


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

   Subscribe/Renew Journal


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.
Subscription Login to verify subscription
User
Notifications
Font Size


Abstract Views: 212

PDF Views: 0




  • Uniqueness and the Convergence of Successive Approximations

Abstract Views: 212  |  PDF Views: 0

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.