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

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  • Sudhakar G. Pandit

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.

Suggested Citation

  • Sudhakar G. Pandit, 1997. "Quadratically converging iterative schemes for nonlinear Volterra integral equations and an application," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-10, January.
    • Handle: RePEc:hin:jnijsa:470243
    DOI: 10.1155/S1048953397000208
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    Cited by:

    1. Torkaman, Soraya & Heydari, Mohammad & Loghmani, Ghasem Barid, 2023. "A combination of the quasilinearization method and linear barycentric rational interpolation to solve nonlinear multi-dimensional Volterra integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 366-397.
    2. Zare, Farideh & Heydari, Mohammad & Loghmani, Ghasem Barid, 2024. "Convergence analysis of an iterative scheme to solve a family of functional Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 477(C).

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