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Quadratically converging iterative schemes for nonlinear Volterra integral equations and an application. (English) Zbl 0881.45004

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.

MSC:

45G10 Other nonlinear integral equations
45L05 Theoretical approximation of solutions to integral equations
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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