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methcalchimplugin-autotooltip__default plugin-autotooltip_bigCalculation methods applied to chemistry

Synopsis (english)

Mathematical prerequisites

Programming bases and tools

* Python programming language * LearnPython.org interactive tutorial with code execution * DataCamp free course "Intro to Python for Data Science" * Python 3 Tutorial, interactive, with code use in web browser * MOOCs (massive open online courses) :
21 Occurrences trouvées, Dernière modification:
ogramming language * [[http://www.learnpython.org/|LearnPython.org]] interactive tutorial with code execution * [[https://www.datacamp.com/courses/i... online courses) : * [[https://www.coursera.org/course/interactivepython|An Introduction to Inter... Beginners)]] (Coursera) * [[https://www.edx.org/course/introduction-computer-science-mitx-6-00-1x
numerical_methods_for_ordinary_differential_equationsplugin-autotooltip__default plugin-autotooltip_bigIntegration of Ordinary Differential Equations

* Ordinary Differential Equations (ODE, ODEs) * Numerical methods for ordinary differential equations * Euler method * Runge-Kutta methods * « most widely known member of the Runge–Kutta family is generally referred to as “RK4”, “classical Runge–Kutta method” or simply as “the Runge–Kutta method »
10 Occurrences trouvées, Dernière modification:
s) * molecular dynamics, [[https://en.wikipedia.org/wiki/Verlet_integration|Verlet integration]] ===... solutions (and codes) : * [[http://www.node99.org/tutorials/ar/]] (RK4) * [[http://www.gribblelab.org/compneuro2012/2_Modelling_Dynamical_Systems.html#orgheadline5]] * [[https://titanlab.org/2010/04/08/lorenz-attractor/]] * [[http://jak
eigenvalues_and_eigenvectorsplugin-autotooltip__default plugin-autotooltip_bigEigenvalues and eigenvectors

* Eigenvalues and eigenvectors * Important matrix properties * Hermitian, orthogonality,...

* Eigenvalue algorithm * Power iteration, a simple numerical algorithm producing a number $\lambda$, the greatest (in absolute value) eigenvalue of a matrix $A$, and the corresponding eigenvector $v$$Av=\lambda v$
6 Occurrences trouvées, Dernière modification:
onal relaxation * //e.g.// [[https://pubs.acs.org/doi/abs/10.1021/ed066p142|Collisional relaxation ... mPy (more portability) * [[https://docs.scipy.org/doc/numpy/reference/routines.linalg.html|numpy.linalg]] * [[https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.ht... ACK]] fortran package) * [[https://docs.scipy.org/doc/scipy/reference/linalg.html|scipy.linalg]]
root-finding_algorithmplugin-autotooltip__default plugin-autotooltip_bigRoot findings : equations f(x) = 0

* Polynomial equations : Bairstow's method is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree * Polynomials in NumPy * polynomial module, including polyroots(c) to compute the roots of a polynomial.

* Bisection method (dichotomy) : very simple and robust method, but relatively slow. It assumes continuity of the function, and obtain one roots. The algorithm is based on a
5 Occurrences trouvées, Dernière modification:
al of arbitrary degree * [[https://docs.scipy.org/doc/numpy/reference/routines.polynomials.html|Polynomials in NumPy]] * [[https://docs.scipy.org/doc/numpy/reference/routines.polynomials.polynomi... ts of Polynomials * Python [[https://docs.scipy.org/doc/numpy/|NumPy]] library : [[https://docs.scipy.org/doc/scipy/reference/|SciPy Reference]] * [[ht
system_of_linear_equationsplugin-autotooltip__default plugin-autotooltip_bigSystem of linear equations

Time_complexityi.e. Theory

* System_of_linear_equations * Gaussian_elimination, Gauss and Gauss-Jordan eliminations (diagonalization, triangularization) * Pivot_element, pivoting * LU_decomposition * Triangular_matrix

* Chapter 2 in the book “Numerical Recipes” : * 2.0 Introduction * 2.1 Gauss-Jordan Elimination
4 Occurrences trouvées, Dernière modification:
d Its Application * Python [[https://docs.scipy.org/doc/numpy/|NumPy]] library : [[https://docs.scipy.org/doc/numpy/reference/index.html|NumPy Reference]] * [[https://docs.scipy.org/doc/numpy/reference/routines.linalg.html|Linear algebra (numpy.linalg)]] : [[https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.solve.
numerical_integrationplugin-autotooltip__default plugin-autotooltip_bigNumerical integration

Error estimation

* Equally spaced methods : * Numerical_integration * Trapezoidal_rule * Newton–Cotes_formulas * Simpson's rule and composite Simpson's rule

* If intervals between interpolation points vary : * Gaussian_quadrature

* Chapter 4 in the book “Numerical Recipes” : Integration of Functions * 4.0 Introduction * 4.1 Classical Formulas for Equally Spaced Abscissas
3 Occurrences trouvées, Dernière modification:
s * Python SciPy library : [[https://docs.scipy.org/doc/scipy/reference/|SciPy Reference]] * [[https://docs.scipy.org/doc/scipy/reference/tutorial/integrate.html|Integ... ntegration calculus compare to [[https://pubs.acs.org/doi/10.1021/acs.jchemed.8b00193|Employing Spreads