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- methcalchim
- * spyder (powerful Python IDE) * includes lot of Python libraries : matplotlib, numpy, scipy, pand... https://jupyter.readthedocs.io/en/latest/|Jupyter official documentation]] * [[https://www.datacam... pyter DataCamp Cheat Sheet]] <note tip>The Microsoft Azure Notebooks environment can be used to execute sample codes, using a professionnal, personnal or student login/account (i.
- system_of_linear_equations
- ====== System of linear equations ====== <note tip>Numerical methods used to solve such problem allow ... ime_complexity]], considering cubic time behavior of standard algorithms and //i.e.// quadratic time s... ition.</note> ===== Theory ===== * [[wp>System_of_linear_equations]] * [[wp>Gaussian_elimination]... on with numpy standard library * measurements of execution time to check cubic complexity ==== 1D
- numerical_methods_for_ordinary_differential_equations
- ====== Integration of Ordinary Differential Equations ====== * [[wp>Ordinary_differential_equation|O... utta methods]] * « most widely known member of the Runge–Kutta family is generally referred to a... ==== <blockquote>« The Lorenz system is a system of ordinary differential equations (the Lorenz equat... ons. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, whe
- root-finding_algorithm
- 0 ====== <note tip> Algorithm used to find roots of an equation use iterations, and a numerical crite... sufficiently accurate value is reached. The rate of convergence depends on the used method and the fu... Some methods (Newton-Raphson) need the derivative of the function f(x). </note> * Polynomial equati... ] is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree * [[htt
- partial_differential_equation
- ====== Numerical solutions of PDE ====== <note warning>In general, the numerical solutions of partial differential equations are obtained by st... ethods developped and implemented in specialized softwares : * Finite element method * Finite volu... ethod * Multigrid methods * ... These methods often make use of variational principles. </note>
- eigenvalues_and_eigenvectors
- bda$, the greatest (in absolute value) eigenvalue of a matrix $A$, and the corresponding eigenvector $... via eigenfunction-eigenvalue expansion: Analysis of a simple case]] Wendell Forst, J. Chem. Educ., 19... ]] Compute the eigenvalues and right eigenvectors of a square array * SciPy (more complete wrapper o... lve an ordinary or generalized eigenvalue problem of a square matrix * [[https://docs.scipy.org/
- numerical_integration
- merical integration ====== <note tip> Calculation of definite integrals implies to replace the functio... timation|Error estimation]] depends on parameters of the method and refinement of spatial grid discretization. It is interesting to check these errors usi... r 4 in the book “Numerical Recipes” : Integration of Functions * 4.0 Introduction * 4.1 Classi