An application of Newton's method to differential and integral equations

DOI10.1017/S1446181100012001zbMath0976.65053MaRDI QIDQ2711361

Miguel A. Hernández, José Manuel Gutiérrez Jimenez

Publication date: 3 July 2001

Published in: The ANZIAM Journal (Search for Journal in Brave)

zbMATH Keywords

Banach spaceserror estimatesNewton's methodintegral equationsdifferential equationssemilocal convergence

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Numerical solutions to equations with nonlinear operators (65J15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Cyclic codes (94B15)

Related Items (1)

The Theory of Kantorovich for Newton’s Method: Conditions on the Second Derivative

Cites Work

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• A new semilocal convergence theorem for Newton's method
• A note on the Kantorovich theorem for Newton iteration
• Differential equations and their applications. An introduction to applied mathematics. 3rd ed
• On the method of tangent hyperbolas in Banach spaces
• A convergence theorem for Newton-like methods in Banach spaces
• Newton's method under mild differentiability conditions with error analysis
• Accessibility Of Solutions By Newton's Method
• A Unified Convergence Theory for a Class of Iterative Processes

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