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methcalchim
33 Occurrences trouvées, Dernière modification :
* spyder (powerful Python IDE) * includes lot of Python libraries : matplotlib, numpy, scipy, pand... = Fundamental numerical methods ==== * [[system_of_linear_equations|Systems of linear equations]] * Diagonalisation and triangularisation * LU d... tures <note tip> Learning outcomes : * Systems of linear equations * failing of the theoretical
system_of_linear_equations
13 Occurrences trouvées, Dernière modification :
====== 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
11 Occurrences trouvées, Dernière modification :
====== 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
11 Occurrences trouvées, Dernière modification :
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
6 Occurrences trouvées, Dernière modification :
====== Numerical solutions of PDE ====== <note warning>In general, the numerical solutions of partial differential equations are obtained by st... grid methods * ... These methods often make use of variational principles. </note> * [[wp>Numeric... ence method]] can be more easliy applied to a lot of classical PDE. In this method, functions are repr
eigenvalues_and_eigenvectors
5 Occurrences trouvées, Dernière modification :
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
5 Occurrences trouvées, Dernière modification :
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