Journal of Applied Mathematics and Stochastic Analysis 
Volume 10 (1997), Issue 2, Pages 169-178
doi:10.1155/S1048953397000208

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

Abstract

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.