دانلود کتاب New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications

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Front Cover
New Numerical Scheme With Newton Polynomial
Copyright
Contents
Preface
Acknowledgments
List of symbols
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 interpolation
2 Two-steps Lagrange polynomial 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 the Caputo–Fabrizio operator
2.3.1 Error analysis with exponential kernel
2.3.2 Numerical illustrations
2.4 Differential equation with the Caputo fractional operator
2.4.1 Error analysis with power-law kernel
2.4.2 Numerical illustrations
2.5 Differential equation with the Atangana–Baleanu operator
2.5.1 Error analysis with the 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 the Caputo fractal–fractional derivative
2.6.2 Numerical illustrations
2.7 Differential equation with fractal–fractional derivative with exponential decay kernel
2.7.1 Error analysis with the Caputo–Fabrizio fractal–fractional derivative
2.7.2 Numerical illustrations
2.8 Differential equation with fractal–fractional derivative with the Mittag-Leffler kernel
2.8.1 Error analysis with the 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 derivative with variable order with exponential decay kernel
2.9.2 Numerical illustrations
2.10 Differential equation with fractal–fractional derivative with variable order with the Mittag-Leffler kernel
2.10.1 Error analysis with fractal–fractional derivative with variable order with Mittag-Leffler kernel
2.10.2 Numerical illustrations
2.11 Differential equation with fractal–fractional derivative with variable order with power-law kernel
2.11.1 Error analysis with fractal–fractional derivative with variable order with power-law kernel
2.11.2 Numerical illustrations
3 Newton interpolation: introduction of the scheme for classical calculus
3.1 Error analysis with classical derivative
3.2 Numerical illustrations
4 Numerical method for fractal differential equations
4.1 Error analysis with fractal derivative
4.2 Numerical illustrations
5 Numerical method for a fractional differential equation with Caputo–Fabrizio derivative
5.1 Error analysis with Caputo–Fabrizio fractional derivative
5.2 Numerical illustrations
6 Numerical method for a fractional differential equation with power-law kernel
6.1 Error analysis with Caputo fractional derivative
6.2 Numerical illustrations
7 Numerical method for a fractional differential equation with the generalized Mittag-Leffler kernel
7.1 Error analysis with the Atangana–Baleanu fractional derivative
7.2 Numerical illustrations
8 Numerical method for a fractal–fractional ordinary differential equation with exponential decay kernel
8.1 Predictor–corrector method for fractal–fractional derivative with the exponential decay kernel
8.2 Error analysis with the Caputo–Fabrizio fractal–fractional derivative
8.3 Numerical illustrations
9 Numerical method for a fractal–fractional ordinary differential equation with power law kernel
9.1 Predictor–corrector method for fractal–fractional derivative with power law kernel
9.2 Error analysis with Caputo fractal–fractional derivative
9.3 Numerical illustrations
10 Numerical method for a fractal–fractional ordinary differential equation with Mittag-Leffler kernel
10.1 Predictor–corrector method for fractal–fractional derivative with the generalized Mittag-Leffler kernel
10.2 Error analysis with the Atangana–Baleanu fractal–fractional derivative
10.3 Numerical illustrations
11 Numerical method for a fractal–fractional ordinary differential equation with variable order with exponential decay kernel
11.1 Numerical illustrations
12 Numerical method for a fractal–fractional ordinary differential equation with variable order with power-law kernel
12.1 Numerical illustrations
13 Numerical method for a fractal–fractional ordinary differential equation with variable order with the generalized Mittag-Leffler kernel
13.1 Numerical illustrations
14 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 the Atangana–Baleanu fractional operator
14.3.1 Numerical illustrations
14.4 Numerical scheme with the Caputo fractional operator
14.4.1 Numerical illustrations
14.5 Numerical scheme with the Caputo–Fabrizio fractional operator
14.5.1 Numerical illustration
14.6 Numerical scheme with the Atangana–Baleanu fractal–fractional operator
14.7 Numerical scheme with the Caputo fractal–fractional operator
14.8 Numerical scheme for Caputo–Fabrizio fractal–fractional operator
14.9 New scheme with fractal–fractional with variable order with exponential decay kernel
14.10 New scheme with fractal–fractional with variable order with the Mittag-Leffler kernel
14.11 New scheme with fractal–fractional with variable order with power-law kernel
15 Application to linear ordinary differential equations
15.1 Linear ordinary differential equations with integer and non-integer orders
15.1.1 A non-homogeneous linear differential equation
15.1.2 Non-homogeneous linear differential equation with the Atangana–Baleanu derivative
15.1.3 Non-homogeneous linear differential equation with the Caputo derivative
15.1.4 Non-homogeneous linear differential equation with fractal–fractional with the exponential law
15.1.5 Non-homogeneous linear differential equation with fractal–fractional derivative with the Mittag-Leffler kernel
16 Application to non-linear ordinary differential equations
16.1 Non-linear ordinary differential equations with integer and non-integer orders
16.1.1 Non-homogeneous nonlinear differential equation with classical derivative
16.1.2 Non-homogeneous non-linear differential equation with Caputo–Fabrizio derivative
16.1.3 Non-homogeneous non-linear differential equation with fractal derivative
16.1.4 Non-homogeneous non-linear differential equation with the fractal–fractional derivative with exponential law
16.1.5 Non-homogeneous non-linear differential equation with fractal–fractional with variable order with power law
17 Application to linear partial differential equations
17.1 Linear partial differential equations with integer and non-integer orders
17.1.1 Linear partial differential equation with the classical derivative
17.1.2 Linear partial differential equation with the fractal derivative
17.1.3 Linear partial differential equation with the Caputo fractional derivative
17.1.4 Linear partial differential equation with the fractal–fractional derivative with the exponential law
17.1.5 Linear partial differential equation with the fractal–fractional with variable order with the Mittag-Leffler kernel
18 Application to non-linear partial differential equations
18.1 Non-linear partial differential equations with integer and non-integer orders
18.1.1 Non-linear partial differential equation with the classical derivative
18.1.2 Non-linear partial differential equation with the fractal derivative
18.1.3 Non-linear partial differential equation with the Caputo fractional derivative
18.1.4 Non-linear partial differential equation with the fractal–fractional with exponential law
18.1.5 Non-linear partial differential equation with the fractal–fractional with variable order with the Mittag-Leffler kernel
19 Application to a system of ordinary differential equations
19.1 System of ordinary differential equations with integer and non-integer orders
19.1.1 A hybrid attractor with the classical derivative
19.1.2 Shaw oscillator with the Caputo fractional derivative
19.1.3 Dengue model with the Atangana–Baleanu fractional derivative
19.1.4 HIV model with fractal–fractional derivative with power law
19.1.5 Ebola model with fractal–fractional derivative with variable order with the exponential law
20 Application to system of non-linear partial differential equations
20.1 System of non-linear partial differential equations
20.1.1 System of non-linear partial differential equations with the classical derivative
20.1.2 System of non-linear partial differential equations with the Atangana–Baleanu derivative
20.1.3 System of non-linear partial differential equations with the Caputo fractional derivative
20.1.4 System of non-linear partial differential equations with the fractal–fractional with the Mittag-Leffler kernel
20.1.5 System of non-linear partial differential equations with fractal–fractional with the power law
A Appendix
AS_Method_for_Chaotic_with_AB_Fractal-Fractional.m
AS_Method_for_Chaotic_with_AB_Fractal-Fractional_with_Variable_Order.m
AS_Method_for_Chaotic_with_AB_Fractional.m
AS_Method_for_Chaotic_with_Caputo_Fractal-Fractional_with_Variable_Order.m
AS_Method_for_Chaotic_with_Caputo_Fractional.m
AS_Method_for_Chaotic_with_CF_Fractal-Fractional_with_Variable_Order.m
AS_Method_for_Chaotic_with_CF_Fractional.m
AS_Method_for_Differential_Equation_with_AB_Fractal-Fractional.m
AS_Method_for_Differential_Equation_with_AB_Fractal-Fractional_with_Variable_Order.m
AS_Method_for_Differential_Equation_with_AB_Fractional.m
AS_Method_for_Differential_Equation_with_Caputo_Fractal-Fractional.m
AS_Method_for_Differential_Equation_with_Caputo_Fractional.m
AS_Method_for_Differential_Equation_with_Caputo_Fractal-Fractional_with_Variable_Order.m
AS_Method_for_Differential_Equation_with_CF_Fractal-Fractional.m
AS_Method_for_Differential_Equation_with_CF_Fractional.m
AS_Method_for_Differential_Equation_with_CF_Fractal-Fractional_with_Variable_Order.m
AS_Method_for_Differential_Equation_with_Classical.m
AS_Method_for_Differential_Equation_with_Fractal.m
AT_Method_for_Chaotic_with_AB_Fractal-Fractional.m
AT_Method_for_Chaotic_with_AB_Fractal-Fractional_with_Variable_Order.m
AT_Method_for_Chaotic_with_AB_Fractional.m
AT_Method_for_Chaotic_with_Caputo_Fractal-Fractional_with_Variable_Order.m
AT_Method_for_Chaotic_with_Caputo_Fractal-Fractional.m
AT_Method_for_Chaotic_with_Caputo_Fractional.m
AT_Method_for_Chaotic_with_CF_Fractal-Fractional.m
AT_Method_for_Chaotic_with_CF_Fractal-Fractional_with_Variable_Order.m
AT_Method_for_Chaotic_with_CF_Fractional.m
AT_Method_for_Differential_Equation_with_AB_Fractal-Fractional.m
AT_Method_for_Differential_Equation_with_AB_Fractal-Fractional_with_Variable_Order.m
AT_Method_for_Differential_Equation_with_AB_Fractional.m
AT_Method_for_Differential_Equation_with_Caputo_Fractal-Fractional_with_Variable_Order.m
AT_Method_for_Differential_Equation_with_Caputo_Fractal-Fractional.m
AT_Method_for_Differential_Equation_with_Caputo_Fractional.m
AT_Method_for_Differential_Equation_with_CF_Fractal-Fractional.m
AT_Method_for_Differential_Equation_with_CF_Fractal-Fractional_with_Variable_Order.m
AT_Method_for_Differential_Equation_with_CF_Fractional.m
AT_Method_for_Differential_Equation_with_Classical.m
AT_Method_for_Differential_Equation_with_Fractal.m
A.1 Supplementary material
References
Index
Back Cover