
New Numerical Scheme with Newton Polynomial
Theory, Methods, and Applications
Description
Key Features
- 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
Readership
Graduate students and researchers in mathematics (pure and applied), engineering, physics, economics
Table of Contents
1 Polynomial Interpolation
1.1 Some Interpolation Polynomials
1.1.1 Bernstein Polynomial
1.1.2 The Newton Polynomial Interpolation
1.1.3 Hermite Interpolation
1.1.4 Cubic Polynomial
1.1.5 B-spline Polynomial
1.1.6 Legendre Polynomial
1.1.7 Chebyshev Polynomial
1.1.8 Lagrange-Sylvester interpolation2 Lagrange Interpolation: Numerical Scheme
2.1 Classical Differential Equation
2.1.1 Numerical Illustrations
2.2 Fractal Differential Equation
2.2.1 Numerical Illustrations
2.3 Differential Equation with Caputo-Fabrizio Operator
2.3.1 Error Analysis with Exponential Kernel
2.3.2 Numerical Illustrations
2.4 Differential Equation with Caputo Fractional Operator
2.4.1 Error Analysis with Power-Law Kernel
2.4.2 Numerical Illustrations
2.5 Differential Equation with Atangana-Baleanu Operator
2.5.1 Error Analysis with Mittag-Leffler Kernel
2.5.2 Numerical Illustrations
2.6 Differential Equation with Fractal-Fractional with Power-Law Kernel
2.6.1 Error Analysis with Caputo Fractal-Fractional Derivative
2.6.2 Numerical Illustrations
2.7 Differential Equation with Fractal-Fractional with Exponential Decay Kernel
2.7.1 Error Analysis with Caputo-Fabrizio Fractal-Fractional Derivative
2.7.2 Numerical Illustrations
2.8 Differential Equation with Fractal-Fractional with Mittag-Leffler Kernel
2.8.1 Error Analysis with Atangana-Baleanu fractal-fractional derivative
2.8.2 Numerical Illustrations
2.9 Differential equation with Fractal-Fractional with Variable Order with Exponential Decay Kernel
2.9.1 Error Analysis with Fractal-Fractional with Variable Order with Exponential Decay Kernel
2.9.2 Numerical Illustrations
2.10 Differential Equation with Fractal-Fractional with Variable Order with Mittag-Leffler Kernel
2.10.1 Error Analysis with Fractal-Fractional with Variable Order with Mittag-Leffler Kernel
2.10.2 Numerical Illustrations
2.11 Differential Equation with Fractal-Fractional with Variable Order with Power-Law Kernel
2.11.1 Error Analysis with Fractal-Fractional with Variable Order with Power-Law Kernel
2.11.2 Numerical Illustrations3 Newton Interpolation: Introduction to New Scheme for Classical Calculus
3.1 Error Analysis with Classical Derivative
3.2 Numerical Illustrations4 New Scheme for Fractal Calculus
4.1 Error Analysis with Fractal Derivative
4.2 Numerical Illustrations5 New Scheme for Fractional Calculus with Exponential Decay Kernel
5.1 Error Analysis with Caputo-Fabrizio Fractional Derivative
5.2 Numerical Illustrations6 New Scheme for Fractional Calculus with Power-Law Kernel
6.1 Error Analysis with Caputo Fractional Derivative
6.2 Numerical Illustrations7 New scheme for fractional calculus with the generalized Mittag-Leffler kernel
7.1 Error Analysis with Atangana-Baleanu fractional derivative
7.2 Numerical Illustrations8 New scheme for fractal-fractional with exponential decay kernel
8.1 Predictor-corrector method for fractal-fractional with the exponential decay kernel
8.2 Error Analysis with Caputo-Fabrizio fractal-fractional derivative
8.3 Numerical Illustrations9 New scheme for fractal-fractional with power law kernel
9.1 Predictor-corrector method for fractal-fractional with power law kernel
9.2 Error Analysis with Caputo fractal-fractional derivative
9.3 Numerical Examples10 New Scheme for Fractal-Fractional with The Generalized Mittag-Leffler Kernel
10.1 Predictor-Corrector Method for Fractal-Fractional with The Generalized Mittag-Leffler Kern
10.2 Error Analysis with Atangana-Baleanu Fractal-Fractional Derivative
10.3 Numerical Illustrations11 New Scheme with Fractal-Fractional with Variable Order with Exponential Decay Kernel
11.1 Numerical Illustrations12 New Scheme with Fractal-Fractional with Variable Order with Power-Law Kernel
12.1 Numerical Illustrations13 New Scheme with Fractal-Fractional with Variable Order with Mittag-Leffler Kernel
13.1 Numerical Illustrations14 Numerical Scheme for Partial Differential Equations with Integer and Non-integer Order
14.1 Numerical Scheme with Classical Derivative
14.1.1 Numerical Illustrations
14.2 Numerical Scheme with Fractal Derivative
14.2.1 Numerical Illustrations
14.3 Numerical Scheme with Atangana-Baleanu Fractional Operator
14.3.1 Numerical Illustrations
14.4 Numerical Scheme with Caputo Fractional Operator
14.4.1 Numerical Illustrations
14.5 Numerical scheme with Caputo-Fabrizio fractional operator
14.5.1 Numerical Illustration
14.6 Numerical Scheme with Atangana-Baleanu Fractal-Fractional Operator
14.7 Numerical Scheme with Caputo Fractal-Fractional Operator
14.8 Numerical Scheme Caputo-Fabrizio Fractal-Fractional Operator
14.9 New Scheme with Fractal-Fractional with Variable Order with Exponential Decay Kernel
14.10New Scheme with Fractal-Fractional with Variable Order with Mittag-Leffler Kernel
14.11New Scheme with Fractal-Fractional with Variable Order with Power-Law Kernel15 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
Product details
- No. of pages: 460
- Language: English
- Copyright: © Academic Press 2021
- Published: June 10, 2021
- Imprint: Academic Press
- eBook ISBN: 9780323858021
- Paperback ISBN: 9780323854481
About the Authors
Abdon Atangana
Affiliations and Expertise
Seda Igret Araz
Affiliations and Expertise
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