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- methcalchim
- n methods applied to chemistry ====== ===== Synopsis (english) ===== ==== Mathematical prerequisites=... start#les_librairies_scientifiques_essentielles|this]] (french) * [[http://matplotlib.org/|Matplotl... * [[http://sympy.org/en/index.html|SymPy]] symbolis maths * [[http://pandas.pydata.org/|Pandas]], data analysis * Pylab, combine Matplotlib, NumPy and SciPy
- numerical_methods_for_ordinary_differential_equations
- ost widely known member of the Runge–Kutta family is generally referred to as "RK4", "classical Runge–... function]] (and equation) * [[wp>Pierre_François_Verhulst|Pierre François Verhulst]] model and non-linearity * bifurcation, period doubling and rout... orenz system ==== <blockquote>« The Lorenz system is a system of ordinary differential equations (the
- system_of_linear_equations
- ve|numpy.linalg.solve]] * Time complexity analysis * Hint : in Python, use the timeit module ==... algorithm ===== What you must have learned in this chapter ===== * Except ill-conditionned, linear... number of arithmetic operations. * The accuracy is determined by the number of numerical figures whi... using these method. * If the coefficient matrix is the same for different systems (only the independ
- root-finding_algorithm
- ept a solution when a sufficiently accurate value is reached. The rate of convergence depends on the u... ions : [[wp>Bairstow's_method|Bairstow's method]] is an efficient algorithm for finding the roots of a... the function, and obtain one roots. The algorithm is based on a [[wp>Loop_invariant|loop invariant]] property : an interval [a, b] is said to bracket a root if f(a) and f(b) have oppo
- eigenvalues_and_eigenvectors
- ion via eigenfunction-eigenvalue expansion: Analysis of a simple case]] Wendell Forst, J. Chem. Educ.,... iondynamicsandma.pdf]],... * normal modes analysis (molecular vibrations) * PCA (principal component analysis) * Schrödinger equation in quantum mechanics, m
- numerical_integration
- by another one (usually a polynomial form) which is a good approximation and easier to compute. [[wp>... and refinement of spatial grid discretization. It is interesting to check these errors using various a
- partial_differential_equation
- re easliy applied to a lot of classical PDE. In this method, functions are represented by their values... ons apply. The [[wp>Heat_equation|heat equation]] is a parabolic partial differential equation that de... 2T}{\partial z^2}\right)$$ * Dimensional analysis, dimensionless numbers,... * Space discretizati