New Numerical Scheme With Newton Polynomial

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New Numerical Scheme With Newton Polynomial

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Author : Abdon Atangana
language : en
Publisher: Academic Press
Release Date : 2021-06-10

New Numerical Scheme With Newton Polynomial written by Abdon Atangana and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-10 with Mathematics categories.

New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications provides a detailed discussion on the underpinnings of the theory, methods and real-world applications of this numerical scheme. The book's authors explore how this efficient and accurate numerical scheme is useful for solving partial and ordinary differential equations, as well as systems of ordinary and partial differential equations with different types of integral operators. Content coverage includes the foundational layers of polynomial interpretation, Lagrange interpolation, and Newton interpolation, followed by new schemes for fractional calculus. Final sections include six chapters on the application of numerical scheme to a range of real-world applications. Over the last several decades, many techniques have been suggested to model real-world problems across science, technology and engineering. New analytical methods have been suggested in order to provide exact solutions to real-world problems. Many real-world problems, however, cannot be solved using analytical methods. To handle these problems, researchers need to rely on numerical methods, hence the release of this important resource on the topic at hand. - Offers an overview of the field of numerical analysis and modeling real-world problems - Provides a deeper understanding and comparison of Adams-Bashforth and Newton polynomial numerical methods - Presents applications of local fractional calculus to a range of real-world problems - Explores new scheme for fractal functions and investigates numerical scheme for partial differential equations with integer and non-integer order - Includes codes and examples in MATLAB in all relevant chapters

Mathematical Analysis Of Groundwater Flow Models

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Author : Abdon Atangana
language : en
Publisher: CRC Press
Release Date : 2022-03-22

Mathematical Analysis Of Groundwater Flow Models written by Abdon Atangana and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-22 with Technology & Engineering categories.

This book provides comprehensive analysis of a number of groundwater issues, ranging from flow to pollution problems. Several scenarios are considered throughout, including flow in leaky, unconfined, and confined geological formations, crossover flow behavior from confined to confined, to semi-confined to unconfined and groundwater pollution in dual media. Several mathematical concepts are employed to include into the mathematical models’ complexities of the geological formation, including classical differential operators, fractional derivatives and integral operators, fractal mapping, randomness, piecewise differential, and integral operators. It suggests several new and modified models to better predict anomalous behaviours of the flow and movement of pollution within complex geological formations. Numerous mathematical techniques are employed to ensure that all suggested models are well-suited, and different techniques including analytical methods and numerical methods are used to derive exact and numerical solutions of different groundwater models. Features: Includes modified numerical and analytical methods for solving new and modified models for groundwater flow and transport Presents new flow and transform models for groundwater transport in complex geological formations Examines fractal and crossover behaviors and their mathematical formulations Mathematical Analysis of Groundwater Flow Models serves as a valuable resource for graduate and PhD students as well as researchers working within the field of groundwater modeling.

Fractional Differential And Integral Operators With Respect To A Function

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Author : Abdon Atangana
language : en
Publisher: Springer Nature
Release Date : 2025-02-11

Fractional Differential And Integral Operators With Respect To A Function written by Abdon Atangana and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-11 with Mathematics categories.

This book explores the fundamental concepts of derivatives and integrals in calculus, extending their classical definitions to more advanced forms such as fractional derivatives and integrals. The derivative, which measures a function's rate of change, is paired with its counterpart, the integral, used for calculating areas and volumes. Together, they form the backbone of differential and integral equations, widely applied in science, technology, and engineering. However, discrepancies between mathematical models and experimental data led to the development of extended integral forms, such as the Riemann–Stieltjes integral and fractional integrals, which integrate functions with respect to another function or involve convolutions with kernels. These extensions also gave rise to new types of derivatives, leading to fractional derivatives and integrals with respect to another function. While there has been limited theoretical exploration in recent years, this book aims to bridge that gap. It provides a comprehensive theoretical framework covering inequalities, nonlinear ordinary differential equations, numerical approximations, and their applications. Additionally, the book delves into the existence and uniqueness of solutions for nonlinear ordinary differential equations involving these advanced derivatives, as well as the development of numerical techniques for solving them.

Numerical Methods For Roots Of Polynomials Part Ii

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Author : J.M. McNamee
language : en
Publisher: Newnes
Release Date : 2013-07-19

Numerical Methods For Roots Of Polynomials Part Ii written by J.M. McNamee and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-19 with Mathematics categories.

Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. - First comprehensive treatment of Root-Finding in several decades with a description of high-grade software and where it can be downloaded - Offers a long chapter on matrix methods and includes Parallel methods and errors where appropriate - Proves invaluable for research or graduate course

Fractional Stochastic Differential Equations

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Author : Abdon Atangana
language : en
Publisher: Springer Nature
Release Date : 2022-04-22

Fractional Stochastic Differential Equations written by Abdon Atangana and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-22 with Mathematics categories.

This book provides a thorough conversation on the underpinnings of Covid-19 spread modelling by using stochastics nonlocal differential and integral operators with singular and non-singular kernels. The book presents the dynamic of Covid-19 spread behaviour worldwide. It is noticed that the spread dynamic followed process with nonlocal behaviours which resemble power law, fading memory, crossover and stochastic behaviours. Fractional stochastic differential equations are therefore used to model spread behaviours in different parts of the worlds. The content coverage includes brief history of Covid-19 spread worldwide from December 2019 to September 2021, followed by statistical analysis of collected data for infected, death and recovery classes.

Mathematical Modeling Computational Intelligence Techniques And Renewable Energy

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Author : Manoj Sahni
language : en
Publisher: Springer Nature
Release Date : 2023-05-08

Mathematical Modeling Computational Intelligence Techniques And Renewable Energy written by Manoj Sahni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-08 with Technology & Engineering categories.

The book is a collection of best selected research papers presented at the Third International Conference on “Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy (MMCITRE 2022),” organized by the University of Technology Sydney, Australia, in association with the Department of Mathematics, Pandit Deendayal Energy University, India, and Forum for Interdisciplinary Mathematics. This book presents new knowledge and recent developments in all aspects of computational techniques, mathematical modeling, energy systems, applications of fuzzy sets and intelligent computing. The book provides innovative works of researchers, academicians and students in the area of interdisciplinary mathematics, statistics, computational intelligence and renewable energy.

Computer Literature Bibliography 1964 1967

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Author : W. W. Youden
language : en
Publisher:
Release Date : 1965

Computer Literature Bibliography 1964 1967 written by W. W. Youden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Computers categories.

Nbs Special Publication

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Author :
language : en
Publisher:
Release Date : 1968

Nbs Special Publication written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Weights and measures categories.

Numerical Methods For Roots Of Polynomials Part Ii

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Author : J.M. McNamee
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-07-19

Numerical Methods For Roots Of Polynomials Part Ii written by J.M. McNamee and has been published by Elsevier Inc. Chapters this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-19 with Mathematics categories.

The zeros of a polynomial can be readily recovered from its linear factors. The linear factors can be approximated by first splitting a polynomial numerically into the product of its two nonconstant factors and then recursively splitting every computed nonlinear factor in similar fashion. For both the worst and average case inputs the resulting algorithms solve the polynomial factorization and root-finding problems within fixed sufficiently small error bounds by using nearly optimal arithmetic and Boolean time, that is using nearly optimal numbers of arithmetic and bitwise operations; in the case of a polynomial with integer coefficients and simple roots we can immediately extend factorization to root isolation, that is to computing disjoint covering discs, one for every root on the complex plane. The presented algorithms compute highly accurate approximations to all roots nearly as fast as one reads the input coefficients. Furthermore, our algorithms allow processor efficient parallel acceleration, which enables root-finding, factorization, and root isolation in polylogarithmic arithmetic and Boolean time. The chapter thoroughly covers the design and analysis of these algorithms, including auxiliary techniques of independent interest. At the end we compare the presented polynomial root-finders with alternative ones, in particular with the popular algorithms adopted by users based on supporting empirical information. We also comment on some promising directions to further progress.

Numerical Continuation Methods

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Author : Eugene L. Allgower
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Numerical Continuation Methods written by Eugene L. Allgower and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.