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New numerical scheme with Newton polynomial. Theory, methods, and applications (to appear). (English) Zbl 07279474
Amsterdam: Elsevier/Academic Press (ISBN 978-0-323-85448-1/pbk). 380 p. (2021).
Publisher’s description: 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. Key features
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
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65Dxx Numerical approximation and computational geometry (primarily algorithms)
65Lxx Numerical methods for ordinary differential equations