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• W4361003072 abstract "The present paper includes the local and semilocal convergence analysis of a fourth-order method based on the quadrature formula in Banach spaces. The weaker hypotheses used are based only on the first Fréchet derivative. The new approach provides the residual errors, number of iterations, convergence radii, expected order of convergence, and estimates of the uniqueness of the solution. Such estimates are not provided in the approaches using Taylor expansions involving higher-order derivatives, which may not exist or may be very expensive or impossible to compute. Numerical examples, including a nonlinear integral equation and a partial differential equation, are provided to validate the theoretical results." @default.
• W4361003072 created "2023-03-30" @default.
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• W4361003072 date "2023-03-27" @default.
• W4361003072 modified "2023-09-30" @default.
• W4361003072 title "A Newton-like Midpoint Method for Solving Equations in Banach Space" @default.
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• W4361003072 doi "https://doi.org/10.3390/foundations3020014" @default.
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