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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 applicati… Read more
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Immediately download your ebook while waiting for your print delivery. No promo code needed.
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.
Graduate students and researchers in mathematics (pure and applied), engineering, physics, economics
1 Polynomial Interpolation1.1 Some Interpolation Polynomials1.1.1 Bernstein Polynomial1.1.2 The Newton Polynomial Interpolation1.1.3 Hermite Interpolation1.1.4 Cubic Polynomial1.1.5 B-spline Polynomial1.1.6 Legendre Polynomial1.1.7 Chebyshev Polynomial1.1.8 Lagrange-Sylvester interpolation
2 Lagrange Interpolation: Numerical Scheme2.1 Classical Differential Equation2.1.1 Numerical Illustrations2.2 Fractal Differential Equation2.2.1 Numerical Illustrations2.3 Differential Equation with Caputo-Fabrizio Operator2.3.1 Error Analysis with Exponential Kernel2.3.2 Numerical Illustrations2.4 Differential Equation with Caputo Fractional Operator2.4.1 Error Analysis with Power-Law Kernel2.4.2 Numerical Illustrations2.5 Differential Equation with Atangana-Baleanu Operator2.5.1 Error Analysis with Mittag-Leffler Kernel2.5.2 Numerical Illustrations2.6 Differential Equation with Fractal-Fractional with Power-Law Kernel2.6.1 Error Analysis with Caputo Fractal-Fractional Derivative2.6.2 Numerical Illustrations2.7 Differential Equation with Fractal-Fractional with Exponential Decay Kernel2.7.1 Error Analysis with Caputo-Fabrizio Fractal-Fractional Derivative2.7.2 Numerical Illustrations2.8 Differential Equation with Fractal-Fractional with Mittag-Leffler Kernel2.8.1 Error Analysis with Atangana-Baleanu fractal-fractional derivative2.8.2 Numerical Illustrations2.9 Differential equation with Fractal-Fractional with Variable Order with Exponential Decay Kernel2.9.1 Error Analysis with Fractal-Fractional with Variable Order with Exponential Decay Kernel2.9.2 Numerical Illustrations2.10 Differential Equation with Fractal-Fractional with Variable Order with Mittag-Leffler Kernel2.10.1 Error Analysis with Fractal-Fractional with Variable Order with Mittag-Leffler Kernel2.10.2 Numerical Illustrations2.11 Differential Equation with Fractal-Fractional with Variable Order with Power-Law Kernel2.11.1 Error Analysis with Fractal-Fractional with Variable Order with Power-Law Kernel2.11.2 Numerical Illustrations
3 Newton Interpolation: Introduction to New Scheme for Classical Calculus3.1 Error Analysis with Classical Derivative3.2 Numerical Illustrations
4 New Scheme for Fractal Calculus4.1 Error Analysis with Fractal Derivative4.2 Numerical Illustrations
5 New Scheme for Fractional Calculus with Exponential Decay Kernel5.1 Error Analysis with Caputo-Fabrizio Fractional Derivative5.2 Numerical Illustrations
6 New Scheme for Fractional Calculus with Power-Law Kernel6.1 Error Analysis with Caputo Fractional Derivative6.2 Numerical Illustrations
7 New scheme for fractional calculus with the generalized Mittag-Leffler kernel7.1 Error Analysis with Atangana-Baleanu fractional derivative7.2 Numerical Illustrations
8 New scheme for fractal-fractional with exponential decay kernel8.1 Predictor-corrector method for fractal-fractional with the exponential decay kernel8.2 Error Analysis with Caputo-Fabrizio fractal-fractional derivative8.3 Numerical Illustrations
9 New scheme for fractal-fractional with power law kernel9.1 Predictor-corrector method for fractal-fractional with power law kernel9.2 Error Analysis with Caputo fractal-fractional derivative9.3 Numerical Examples
10 New Scheme for Fractal-Fractional with The Generalized Mittag-Leffler Kernel10.1 Predictor-Corrector Method for Fractal-Fractional with The Generalized Mittag-Leffler Kern10.2 Error Analysis with Atangana-Baleanu Fractal-Fractional Derivative10.3 Numerical Illustrations
11 New Scheme with Fractal-Fractional with Variable Order with Exponential Decay Kernel11.1 Numerical Illustrations
12 New Scheme with Fractal-Fractional with Variable Order with Power-Law Kernel12.1 Numerical Illustrations
13 New Scheme with Fractal-Fractional with Variable Order with Mittag-Leffler Kernel13.1 Numerical Illustrations
14 Numerical Scheme for Partial Differential Equations with Integer and Non-integer Order14.1 Numerical Scheme with Classical Derivative14.1.1 Numerical Illustrations14.2 Numerical Scheme with Fractal Derivative14.2.1 Numerical Illustrations14.3 Numerical Scheme with Atangana-Baleanu Fractional Operator14.3.1 Numerical Illustrations14.4 Numerical Scheme with Caputo Fractional Operator14.4.1 Numerical Illustrations14.5 Numerical scheme with Caputo-Fabrizio fractional operator14.5.1 Numerical Illustration14.6 Numerical Scheme with Atangana-Baleanu Fractal-Fractional Operator14.7 Numerical Scheme with Caputo Fractal-Fractional Operator14.8 Numerical Scheme Caputo-Fabrizio Fractal-Fractional Operator14.9 New Scheme with Fractal-Fractional with Variable Order with Exponential Decay Kernel14.10New Scheme with Fractal-Fractional with Variable Order with Mittag-Leffler Kernel14.11New Scheme with Fractal-Fractional with Variable Order with Power-Law Kernel
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
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