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
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.