New Numerical Scheme with Newton Polynomial (eBook)

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

Dr. Atangana is Academic Head of Department and Professor of Applied Mathematics at the University of the Free State, Bloemfontein, Republic of South Africa. He obtained his honours and master's degrees from the Department of Applied Mathematics at the UFS with distinction. He obtained his PhD in applied mathematics from the Institute for Groundwater Studies.
He serves as an editor for 20 international journals and lead guest editor in 10 journals and is also a reviewer of more than 200 international accredited journals. His research interests are methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modelling.
Prof Atangana is the founder of fractional calculus with non-local and non-singular kernels popular in applied mathematics today. Since 2013, he has published in 250 international accredited journals of applied mathematics, applied physics, geo-hydrology and biomathematics. He is also the single author of two books in Academic Press Elsevier and a co-author of a book published in springer and author of more than 20 chapters in books. He has graduated 7 PhD and 20 masters students, and 6 postdoc fellows.

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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