New Numerical Scheme with Newton Polynomial

Theory, Methods, and Applications

Abdon Atangana, Seda ??ret Araz

• Publisher: Academic Press
• Year: 2021
• ISBN:
  9780323858021
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• Acknowledgments
• List of symbols
• 1: Polynomial interpolation
• 2: Two-steps Lagrange polynomial interpolation: numerical scheme
• 3: Newton interpolation: introduction of the scheme for classical calculus
• 4: Numerical method for fractal differential equations
• 5: Numerical method for a fractional differential equation with Caputo–Fabrizio derivative
• 6: Numerical method for a fractional differential equation with power-law kernel
• 7: Numerical method for a fractional differential equation with the generalized Mittag-Leffler kernel
• 8: Numerical method for a fractal–fractional ordinary differential equation with exponential decay kernel
• 9: Numerical method for a fractal–fractional ordinary differential equation with power law kernel
• 10: Numerical method for a fractal–fractional ordinary differential equation with Mittag-Leffler kernel
• 11: Numerical method for a fractal–fractional ordinary differential equation with variable order with exponential decay kernel
• 12: Numerical method for a fractal–fractional ordinary differential equation with variable order with power-law kernel
• 13: Numerical method for a fractal–fractional ordinary differential equation with variable order with the generalized Mittag-Leffler kernel
• 14: Numerical scheme for partial differential equations with integer and non-integer order
• 15: Application to linear ordinary differential equations
• 16: Application to non-linear ordinary differential equations
• 17: Application to linear partial differential equations
• 18: Application to non-linear partial differential equations
• 19: Application to a system of ordinary differential equations
• 20: Application to system of non-linear partial differential equations
• A: Appendix
• References
• Index