Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 2, Pages 169-178

Quadratically converging iterative schemes for nonlinear Volterra integral equations and an application

Sudhakar G. Pandit

Winston-Salem State University, Department of Mathematics, Winston-Salem 27110, NC, USA

Received 1 March 1996; Revised 1 September 1996

Copyright © 1997 Sudhakar G. Pandit. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A generalized quasilinear technique is employed to derive iterative schemes for nonlinear Volterra integral equations under various monotonicity and convexity (concavity) conditions on the kernels. The iterates in the schemes are linear, and converge monotonically, uniformly and quadratically to the unique solution. An application to a boundary-layer theory problem and examples illustrating the results are presented.