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.
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Table of Contents
1. Polynomial Interpolation2. Lagrange Interpolation: Numerical Scheme3. Newton Interpolation: Introduction to New Scheme for Classical Calculus4. New Scheme for Fractal Calculus5. New Scheme for Fractional Calculus with Exponential Decay Kernel6. New Scheme for Fractional Calculus with Power-Law Kernel7. New scheme for fractional calculus with the generalized Mittag-Leffler kernel8. New scheme for fractal-fractional with exponential decay kernel9. New scheme for fractal-fractional with power law kernel10. New Scheme for Fractal-Fractional with The Generalized Mittag-Leffler Kernel11. New Scheme with Fractal-Fractional with Variable Order with Exponential Decay Kernel12. New Scheme with Fractal-Fractional with Variable Order with Power-Law Kernel13. New Scheme with Fractal-Fractional with Variable Order with Mittag-Leffler Kernel14. Numerical Scheme for Partial Differential Equations with Integer and Non-integer Order15. Application to Linear Ordinary Differential Equations16. Application to Nonlinear Ordinary Differential Equations17. Application to Linear Partial Differential Equations18. Application to Nonlinear Partial Differential Equations19. Application to System of Ordinary Differential Equations20. Application to System of Nonlinear Partial Differential Equations
