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- methcalchim
- try ====== ===== Synopsis (english) ===== ==== Mathematical prerequisites==== ==== Programming bases ... tps://www.anaconda.com/download/]] * Includes these tools : * Jupyter notebook (interactive w... Den Kasyanov (Medium) * [[https://jupyter.readthedocs.io/en/latest/|Jupyter official documentation]... t-sheet|Jupyter DataCamp Cheat Sheet]] <note tip>The Microsoft Azure Notebooks environment can be used
- numerical_methods_for_ordinary_differential_equations
- a methods]] * « most widely known member of the Runge–Kutta family is generally referred to as "R... K4", "classical Runge–Kutta method" or simply as "the Runge–Kutta method » * [[wp>Runge–Kutta_metho... egration]] ==== Lorenz system ==== <blockquote>« The Lorenz system is a system of ordinary differential equations (the Lorenz equations, note it is not Lorentz) first s
- partial_differential_equation
- solutions of PDE ====== <note warning>In general, the numerical solutions of partial differential equat... * Spectral method * Multigrid methods * ... These methods often make use of variational principle... erical partial differential equations]] However, the [[wp>Finite_difference_method|finite difference m... PDE. In this method, functions are represented by their values at certain grid points and derivatives a
- system_of_linear_equations
- e solutions using LU decomposition.</note> ===== Theory ===== * [[wp>System_of_linear_equations]] ... #Forward_and_back_substitution]] * Chapter 2 in the book "Numerical Recipes" : * 2.0 Introduction... e complexity analysis * Hint : in Python, use the timeit module ===== Jupyter notebooks ===== * ... plexity ==== 1D problems with neigbours ==== * Thermal diffusion and chemical diffusion (transient o
- root-finding_algorithm
- on when a sufficiently accurate value is reached. The rate of convergence depends on the used method and the function f(x). Some methods (Newton-Raphson) need the derivative of the function f(x). </note> * Pol
- eigenvalues_and_eigenvectors
- numerical algorithm producing a number $\lambda$, the greatest (in absolute value) eigenvalue of a matrix $A$, and the corresponding eigenvector $v$, such that $Av=\lam... antum mechanics, molecular orbitals (Hartree–Fock theory) ===== Python libraries ===== * NumPy (more... ted/numpy.linalg.eig.html|linalg.eig(a)]] Compute the eigenvalues and right eigenvectors of a square ar
- numerical_integration
- culation of definite integrals implies to replace the function by another one (usually a polynomial form) which is a good approximation and easier to comput... ation|Error estimation]] depends on parameters of the method and refinement of spatial grid discretization. It is interesting to check these errors using various algorithm and mesh resolut