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A modified quasilinearization method for fractional differential equations and its applications
(Elsevier Inc. usjcs@elsevier.com, 2015) Vijesh, V.; Roy, R.; Godavarma, G.
Abstract In this paper, we prove an existence and uniqueness theorem for solving the nonlinear fractional differential equation of Caputo's type of order q ? (0, 1] using the method of modified quasilinearization. The main theorem has been illustrated numerically using appropriate examples which shows that the proposed quasilinearization method is robust and easy to apply. © 2015 Elsevier Inc.
Unified convergence analysis of a class of iterative methods
(Springer, 2025) M, M.; George, S.; Godavarma, G.
In this paper, unified convergence analyses for a class of iterative methods of order three, five, and six are studied to solve the nonlinear systems in Banach space settings. Our analysis gives the number of iterations needed to achieve the given accuracy and the radius of the convergence ball precisely using weaker conditions on the involved operator. Various numerical examples have been taken to illustrate the proposed method, and the theoretical convergence has been validated via these examples. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.