Adam Moulton method

https://souravrohan.wordpress.com/2011/06/05/adam-moulton-method/

Adam Moulton method

FORTRAN CODE FOR SOLVING An IVP USING Adam Moulton  4-STEP IMPLICIT METHOD:

PARAMETER(M=10)
OPEN(33,FILE=’INP14.DAT’)
OPEN(34,FILE=’OUP14.DAT’)
READ(33,*)A,B,H,W0
CALL AM(A,B,H,W0,M)
END PROGRAM

SUBROUTINE AM(A,B,H,W0,M)
REAL K1,K2,K3,K4,W(M),T(M),N
WRITE(34,10)
10 FORMAT(2X,’X’,9X,’EXACT’,12X,’AMW(I)’,10X,’ERR’)
N=(B-A)/H
W(0)=W0
T(0)=A
WRITE(34,11)T(0),G(T(0)),W(0), ABS(G(T(0))-W(0))
11 FORMAT(2X,F4.2,3(4X,F12.8))

DO I=1,4
K1=H*F(T(I-1),W(I-1))
K2=H*F(T(I-1)+H/2,W(I-1)+K1/2)
K3=H*F(T(I-1)+H/2,W(I-1)+K2/2)
K4=H*F(T(I-1)+H,W(I-1)+K3)
W(I)=W(I-1)+(K1+2*K2+2*K3+K4)/6.0
T(I)=A+I*H
WRITE(34,11)T(I),G(T(I)),W(I), ABS(G(T(I))-W(I))
END DO
DO I=3,N-1
T(I+1)=A+(I+1)*H
W(I+1)=W(I)+(H/720)*(251*F(T(I+1),W(I+1))+646*F(T(I),W(I))-264*F(T(I-1),W(I-1))+106*F(T(I-2),W(I-2))-19*F(T(I-3),W(I-3)))
WRITE(34,11)T(I+1),G(T(I+1)),W(I+1), ABS(G(T(I+1))-W(I+1))
END DO
END SUBROUTINE

FUNCTION F(T,Y)
F=COS(2*T)+SIN(3*T)
RETURN
END

FUNCTION G(T)
G=SIN(2*T)/2.0-(COS(3*T)-4)/3.0
RETURN
END

inputs:
0
2
0.2
0.5

program name:

outputs:
X EXACT AMW(I) ERR
0.00 1.00000000 1.00000000 0.00000003
0.20 1.25293064 1.15557957 0.09735110
0.40 1.57122552 1.39189768 0.17932783
0.60 1.87508702 1.64209783 0.23298915
0.80 2.07891798 1.82905316 0.24986494
0.80 2.07891798 1.82908905 0.24982905
1.00 2.11797953 1.89059699 0.22738262

SEE NUMERICAL ANALYSIS (7TH EDITION) BY BURDEN
PAGE 295 TO KNOW MORE………………………………

Modules for Numerical Methods & Numerical Analysis

 Modules for Numerical Methods & Numerical Analysis
John H. Mathews, Ph. D.
Emeritus Prof. of Mathematics
California State Univ. Fullerton
Fullerton, California 92834

http://mathfaculty.fullerton.edu/mathews/n2003/NumericalUndergradMod.html


Numerical Analysis - Numerical Methods
Modules

Calculus and Fundamentals

1. Calculus Review
2. Big "O" Truncation Error
3. Complex Numbers
4. Complex Functions
5. Using MATLAB for Numerical Analysis

The Solution of Nonlinear Equations f(x) = 0

1. Fixed Point Iteration
2. Bisection Method
3. False Position or Regula Falsi Method
4. Newton-Raphson Method
5. Secant Method
6. Muller's Method
7. Aitken's Method & Steffensen's Acceleration
8. Accelerated & Modified Newton-Raphson
9. Improved Newton Method
10. Halley's Method
11. Horner's Method
12. Lin-Bairstow Method
13. Brent's Method
14. Graeffe's Method
15. Nonlinear Systems
16. Broyden's Method

The Solution of Linear Systems AX = B

1. Triangular Systems and Back Substitution
2. Gauss-Jordan Elimination and Pivoting
3. Tri-Diagonal Matrices
4. Inverse Matrix
5. LU Factorization
6. Cholesky, Doolittle and Crout Factorizations
7. Jacobi and Gauss-Seidel Iteration
8. Successive Over Relaxation - SOR
9. Pivoting Methods
10. Iterative Refinement
11. Row Reduced Echelon Form
12. Homogeneous Linear Systems
13. Kirchoff's Law
14. Leontief Model
15. Linear Programming-Simplex Method

Interpolation and Polynomial Approximation

1. Maclaurin and Taylor Series
2. Lagrange Polynomial Interpolation and Approximation
3. Newton Interpolation Polynomial
4. Hermite Polynomial Interpolation
5. Cubic Splines
6. B-Splines
7. Bézier Curves Bézier Curves
8. Chebyshev Approximation Polynomial
9. Pade Approximation
10. Rational Approximation
11. Aitken's and Neville's Interpolation
12. Legendre Polynomials
13. The Tangent Parabola
14. Catenary

Curve Fitting

1. Least Squares Lines
2. Least Squares Polynomials
3. Nonlinear Curve Fitting
4. Logistic Curve
5. FFT and Trigonometric Polynomials 
6. Conic Fit
7. Circle of Curvature

Numerical Differentiation

1. Numerical Differentiation 
2. Richardson Extrapolation
3. Derive Numerical Differentiation Formulae

Numerical Integration

1. Riemann Sums
2. Midpoint Rule
3. Newton-Cotes Integration
4. Trapezoidal Rule for Numerical Integration
5. Simpson's Rule for Numerical Integration
6. Simpson's 3/8 Rule for Numerical Integration
7. Boole's Rule
8. Romberg Integration
9. Adaptive Simpson's Rule
10. Gauss-Legendre Quadrature
11. Cubic Spline Quadrature  
12. Monte Carlo Pi
13. Monte Carlo Integration
14. 2D Trapezoidal and Simpson Rules

Solution of Differential Equations

1. Euler's Method for ODE's
2. Taylor Series Method for ODE's
3. Runge-Kutta Method
4. Runge-Kutta-Fehlberg Method
5. Adams-Bashforth-Moulton Method
6. Milne-Simpson's Method
7. Predictor-Corrector Methods
8. Shooting Methods for ODE's
9. Finite Difference Method for ODE's
10. Galerkin's Method
11. Painleve Property
12. Lotka-Volterra Model
13. Pendulum
14. Projectile Motion
15. Lorenz Attractor
16. van der Pol System
17. Harvesting Model
18. Frobenius Series Solution
19. Picard Iteration
20. Spring-Mass Systems

Solution of Partial Differential Equations

1. Finite Difference Method
2. Crank-Nicolson Method
3. Elliptic PDE's

Eigenvalues and Eigenvectors

1. Eigenvalues and Eigenvectors
2. Power method
3. Jacobi method
4. Householder Transformations
5. QR method
6. Compartment Model
7. Earthquake Model
8. Matrix Exponential
9. Faddeev-Leverrier Method 
10. Hessenberg Factorization

Numerical Optimization

1. Golden Ratio Search
2. Fibonacci Search
3. Quadratic Interpolative Search
4. Nelder Mead Method
5. Powell's Method
6. Steepest Descent - Gradient Search
7. Newton's Search Method

Return to Numerical Methods - Numerical Analysis

Inteligencia Artificial - Aprendizaje automático - Amazon - Colab - Azure Notebooks

AWS - AMAZON
Aprendizaje automático: científico de datos Conozca en profundidad la matemática, las ciencias y las estadísticas detrás del aprendizaje automático

https://aws.amazon.com/es/training/learning-paths/machine-learning/data-scientist/

COLAB

Machine learning development: the end-to-end cycle

https://cloud.google.com/ai-platform/

AZURE Notebooks

Walkthrough of Azure Notebooks

• 4 (OF 5)
• 15 MIN
• BEGINNER

A walkthrough of how programming in Azure Notebooks works - we introduce features and labels, and do a short programming exercise.

https://aischool.microsoft.com/en-us/machine-learning/learning-paths/ml-crash-course/introduction-to-ai/walkthrough-of-azure-notebooks

IELTS Exams Preparation - Подготовка к экзаменам IELTS

IELTS Exams Preparation

Подготовка к экзаменам IELTS

https://www.examenglish.com/

https://ieltsonlinetests.com/collection/ielts-mock-test-2018-january

apps online - cloud virtualization technologies

apps online - cloud virtualization technologies

Turbo

Last but perhaps the most powerful service is Turbo – a virtual platform for running, testing and deploying Windows apps and services in the cloud. The apps run through a browser extension installed in your web browser that works without admin privileges, thus eliminating installation or dependencies issues.

Manymo

If you’re looking for an Android emulator in the cloud, then Manymo would suit you the best. This emulator lets you test or run Android apps directly in the web browser, hence you can experience and enjoy apps even without having an Android device.

Cameyo

Of all the solutions in this list, Cameyo is the only service that offers most features for free (with limitations, of course).

Appetize

If you want to try out or test mobile apps in the browser, then Appetize is the tool for you. This web service allows previewing, using and testing apps on a cloud simulator directly from the browser.

rollApp

Out of all such web services I’ve tried out, rollApp excels in features and stability over others in this list. An online virtualization platform, rollApp is very easy to sign up, use and connect to your cloud storage.

Six easy ways to run your Jupyter Notebook in the cloud - Шесть простых способов запустить ноутбук Jupyter в облаке

Six easy ways to run your Jupyter Notebook in the cloud - Шесть простых способов запустить ноутбук Jupyter в облаке

https://www.dataschool.io/cloud-services-for-jupyter-notebook/

Getting Started With Google Colab A Simple Tutorial for the Frustrated and Confused

Getting Started With Google Colab

A Simple Tutorial for the Frustrated and Confused

 

https://towardsdatascience.com/getting-started-with-google-colab-f2fff97f594c