Intelligent numerical methods Applications to Fractional Calculus George A. Anastassiou
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Product details:
- ISBN-10 : 3319800035
- ISBN-13 : 978-3319800035
- Author:
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.
Table of contents:
1. Newton-Like Methods on Generalized Banach Spaces and Fractional Calculus
2. Semilocal Convegence of Newton-Like Methods and Fractional Calculus
3. Convergence of Iterative Methods and Generalized Fractional Calculus
4. Fixed Point Techniques and Generalized Right Fractional Calculus
5. Approximating Fixed Points and k-Fractional Calculus
6. Iterative Methods and Generalized g-Fractional Calculus
7. Unified Convergence Analysis for Iterative Algorithms and Fractional Calculus
8. Convergence Analysis for Extended Iterative Algorithms and Fractional and Vector Calculus
9. Convergence Analysis for Extended Iterative Algorithms and Fractional Calculus
10. Secant-Like Methods and Fractional Calculus
11. Secant-Like Methods and Modified g-Fractional Calculus
12. Secant-Like Algorithms and Generalized Fractional Calculus
13. Secant-Like Methods and Generalized g-Fractional Calculus of Canavati-Type
14. Iterative Algorithms and Left-Right Caputo Fractional Derivatives
15. Iterative Methods on Banach Spaces with a Convergence Structure and Fractional Calculus
16. Inexact Gauss-Newton Method for Singular Equations
17. The Asymptotic Mesh Independence Principle
18. Ball Convergence of a Sixth Order Iterative Method
19. Broyden’s Method with Regularly Continuous Divided Differences
20. Left General Fractional Monotone Approximation
21. Right General Fractional Monotone Approximation Theory
22. Left Generalized High Order Fractional Monotone Approximation
23. Right Generalized High Order Fractional Monotone Approximation
24. Advanced Fractional Taylor’s Formulae
25. Generalized Canavati Type Fractional Taylor’s Formulae
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