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- methcalchim
- ====== Calculation methods applied to chemistry ====== ===== Synopsis (english) ===== ==== Mathematical prerequisites==== ==== Programming bases and tools ==== * Python progra
- system_of_linear_equations
- ve|numpy.linalg.solve]] * Time complexity analysis * Hint : in Python, use the timeit module ==... html/notebooks/calculation_methods_applied_to_chemistry/Gauss-Jordan-01.ipynb]] ===== Exercices and a... cices : * write a python function for diagonalisation with partial pivoting * random numbers → linear systems * comparison with numpy standard library * measurements
- numerical_methods_for_ordinary_differential_equations
- ost widely known member of the Runge–Kutta family is generally referred to as "RK4", "classical Runge–... hemical kinetics * population dynamics, [[wp>Logistic_function|Logistic function]] (and equation) * [[wp>Pierre_François_Verhulst|Pierre François Verhulst]] model and non
- eigenvalues_and_eigenvectors
- bda v$. * LR algorithm, developed by Heinz Rutishauser (1958 ?) * [[wp>QR_algorithm|QR algorithm]] ===== Applications ===== * collisional relaxation * //e.g.// [[https://pubs.acs.org/doi/abs/10.1021/ed066p142|Collisional relaxation via eigenfunction-eigenvalue expansion: Analysis of a simple case]] Wendell Forst, J. Chem. Educ.,
- 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... ) to compute the roots of a polynomial. * [[wp>Bisection_method|Bisection method]] (dichotomy) : very simple and robust method, but relatively slow. It
- numerical_integration
- by another one (usually a polynomial form) which is a good approximation and easier to compute. [[wp>... ers of the method and refinement of spatial grid discretization. It is interesting to check these errors using various algorithm and mesh resolution. </no... * 4.1 Classical Formulas for Equally Spaced Abscissas * 4.2 Elementary Algorithms * 4.5 Gaus
- 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 describes the distribution of heat (or variation in temperature) in... 2T}{\partial z^2}\right)$$ * Dimensional analysis, dimensionless numbers,... * Space discretizati