New Numerical Scheme with Newton Polynomial: Theory, Methods, and 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 and, to handle these problems, researchers need to rely on numerical methods. Mathematicians have developed several numerical schemes, some very efficient and user-friendly, each with limitations, disadvantages and advantages. Some of these numerical schemes are based on polynomial interpolation, for example the Adams-Basforth is based on the Lagrange, spline polynomial, and many others. A numerical method that provides an accurate and easy-to-use solution is, therefore, welcome. While the well-known Adams-Bashforth numerical method is highly used, it is important to note that this numerical method was constructed using the Lagrange polynomial which is well-known to be less accurate than the Newton polynomial. A numerical method based on Newton will therefore be more accurate than that based on Lagrange. New Numerical Scheme with Newton Polynomial: Theory, Methods and Applications is devoted to the detailed discussion underpinning the theory, methods and real-world applications of this numerical scheme. The 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. The final section includes six chapters exploring the application of the numerical scheme to a broad range of real-world applications. The intended audience includes postgraduate students including masters, PhD, and postdoctoral students in applied mathematics, and across all fields of engineering where numerical schemes are used when analytical models cannot be employed. Offers an overview of the field of numerical analysis and modeling real-world problemsProvides a deeper understanding and comparison of Adams-Bashforth and Newton polynomial numerical methodsPresents applications of local fractional calculus to a range of real-world problemsExplores new scheme for fractal functions and investigates numerical scheme for partial differential equations with integer and non-integer orderIncludes codes and examples in MATLAB in all relevant chapters INDICE: 1. Polynomial Interpolation 2. Lagrange Interpolation: Numerical Scheme 3. Newton Interpolation: Introduction to New Scheme for Classical Calculus 4. New Scheme for Fractal Calculus 5. New Scheme for Fractional Calculus with Exponential Decay Kernel 6. New Scheme for Fractional Calculus with Power-Law Kernel 7. New scheme for fractional calculus with the generalized Mittag-Leffler kernel 8. New scheme for fractal-fractional with exponential decay kernel 9. New scheme for fractal-fractional with power law kernel 10. New Scheme for Fractal-Fractional with The Generalized Mittag-Leffler Kernel 11. New Scheme with Fractal-Fractional with Variable Order with Exponential Decay Kernel 12. New Scheme with Fractal-Fractional with Variable Order with Power-Law Kernel 13. New Scheme with Fractal-Fractional with Variable Order with 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 Nonlinear Ordinary Differential Equations 17. Application to Linear Partial Differential Equations 18. Application to Nonlinear Partial Differential Equations 19. Application to System of Ordinary Differential Equations 20. Application to System of Nonlinear Partial Differential Equations

• ISBN: 978-0-323-85448-1
• Editorial: Academic Press
• Encuadernacion: Rústica
• Páginas: 380
• Fecha Publicación: 01/02/2021
• Nº Volúmenes: 1
• Idioma: Inglés