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 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
