Anastassiou, George A.
Intelligent Numerical Methods: Applications to Fractional Calculus [electronic resource] / by George A. Anastassiou, Ioannis K. Argyros. - 1st ed. 2016. - XVI, 423 p. 2 illus. in color. online resource. - Studies in Computational Intelligence, 624 1860-9503 ; . - Studies in Computational Intelligence, 624 .
Newton-Like Methods on Generalized Banach Spaces and Fractional Calculus -- Semilocal Convegence of Newton-Like Methods and Fractional Calculus -- Convergence of Iterative Methods and Generalized Fractional Calculus -- Fixed Point Techniques And Generalized Right Fractional Calculus -- Approximating Fixed Points And K-Fractional Calculus -- Iterative Methods And Generalized G-Fractional Calculus -- Unified Convergence Analysis For Iterative Algorithms And Fractional Calculus -- Convergence Analysis For Extended Iterative Algorithms And Fractional And Vector Calculus -- Convergence Analysis For Extended Iterative Algorithms And Fractional Calculus -- Secant-Like Methods And Fractional Calculus -- Secant-Like Methods And Modified G- Fractional Calculus -- Secant-Like Algorithms And Generalized Fractional Calculus -- Secant-Like Methods And Generalized G-Fractional Calculus Of Canavati-Type -- Iterative Algorithms And Left-Right Caputo Fractional Derivatives -- Iterative Methods On Banach Spaces With A Convergence Structure And Fractional Calculus -- Inexact Gauss-Newton Method For Singular Equations -- The Asymptotic Mesh Independence Principle -- Ball Convergence Of A Sixth Order Iterative Method -- Broyden’s Method With Regularily Continuous Divided Differences -- Left General Fractional Monotone Approximation -- Right General Fractional Monotone Approximation Theor -- Left Generalized High Order Fractional Monotone Approximation -- Right Generalized High Order Fractional Monotone Approximation -- Advanced Fractional Taylor’s Formulae -- Generalized Canavati Type Fractional Taylor’s Formulae.
In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.
9783319267210
10.1007/978-3-319-26721-0 doi
Computational intelligence.
Artificial intelligence.
Mathematics—Data processing.
Dynamics.
Nonlinear theories.
Computational Intelligence.
Artificial Intelligence.
Computational Science and Engineering.
Applied Dynamical Systems.
Q342
006.3
Intelligent Numerical Methods: Applications to Fractional Calculus [electronic resource] / by George A. Anastassiou, Ioannis K. Argyros. - 1st ed. 2016. - XVI, 423 p. 2 illus. in color. online resource. - Studies in Computational Intelligence, 624 1860-9503 ; . - Studies in Computational Intelligence, 624 .
Newton-Like Methods on Generalized Banach Spaces and Fractional Calculus -- Semilocal Convegence of Newton-Like Methods and Fractional Calculus -- Convergence of Iterative Methods and Generalized Fractional Calculus -- Fixed Point Techniques And Generalized Right Fractional Calculus -- Approximating Fixed Points And K-Fractional Calculus -- Iterative Methods And Generalized G-Fractional Calculus -- Unified Convergence Analysis For Iterative Algorithms And Fractional Calculus -- Convergence Analysis For Extended Iterative Algorithms And Fractional And Vector Calculus -- Convergence Analysis For Extended Iterative Algorithms And Fractional Calculus -- Secant-Like Methods And Fractional Calculus -- Secant-Like Methods And Modified G- Fractional Calculus -- Secant-Like Algorithms And Generalized Fractional Calculus -- Secant-Like Methods And Generalized G-Fractional Calculus Of Canavati-Type -- Iterative Algorithms And Left-Right Caputo Fractional Derivatives -- Iterative Methods On Banach Spaces With A Convergence Structure And Fractional Calculus -- Inexact Gauss-Newton Method For Singular Equations -- The Asymptotic Mesh Independence Principle -- Ball Convergence Of A Sixth Order Iterative Method -- Broyden’s Method With Regularily Continuous Divided Differences -- Left General Fractional Monotone Approximation -- Right General Fractional Monotone Approximation Theor -- Left Generalized High Order Fractional Monotone Approximation -- Right Generalized High Order Fractional Monotone Approximation -- Advanced Fractional Taylor’s Formulae -- Generalized Canavati Type Fractional Taylor’s Formulae.
In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.
9783319267210
10.1007/978-3-319-26721-0 doi
Computational intelligence.
Artificial intelligence.
Mathematics—Data processing.
Dynamics.
Nonlinear theories.
Computational Intelligence.
Artificial Intelligence.
Computational Science and Engineering.
Applied Dynamical Systems.
Q342
006.3