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methcalchimplugin-autotooltip__default plugin-autotooltip_bigCalculation methods applied to chemistry

Synopsis (english)

Mathematical prerequisites

Programming bases and tools

* Python programming language * interactive tutorial with code execution * DataCamp free course "Intro to Python for Data Science" * Python 3 Tutorial, interactive, with code use in web browser * MOOCs (massive open online courses) :
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omplexity * "divide by zero" errors and pivot solutions * extension towards the matrix inversion ... ods_for_ordinary_differential_equations|Numerical solutions of ODE]] * principe de discrétisation, méthode ... DE) === [[partial_differential_equation|Numerical solutions of PDE]] * Domaine d'application des équations ...]], learning bioinformatics by problem solutions * Machine Learning * Scikit-learn * [
numerical_methods_for_ordinary_differential_equationsplugin-autotooltip__default plugin-autotooltip_bigIntegration of Ordinary Differential Equations

* Ordinary Differential Equations (ODE, ODEs) * Numerical methods for ordinary differential equations * Euler method * Runge-Kutta methods * « most widely known member of the Runge–Kutta family is generally referred to as “RK4”, “classical Runge–Kutta method” or simply as “the Runge–Kutta method »
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y Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditio... ticular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resembl... range_attractor|Strange attractor]] * Numerical solutions (and codes) : * [[
partial_differential_equationplugin-autotooltip__default plugin-autotooltip_bigNumerical solutions of PDE

* Finite element method * Finite volume method * Boundary element method * Spectral method * Multigrid methods * ...

* Numerical partial differential equations

However, the finite difference method can be more easliy applied to a lot of classical PDE. In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.$$\frac{\partial T}{\partial t} = \kappa\left(\frac{…
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====== Numerical solutions of PDE ====== <note warning>In general, the numerical solutions of partial differential equations are obtained by
system_of_linear_equationsplugin-autotooltip__default plugin-autotooltip_bigSystem of linear equations

Time_complexityi.e. Theory

* System_of_linear_equations * Gaussian_elimination, Gauss and Gauss-Jordan eliminations (diagonalization, triangularization) * Pivot_element, pivoting * LU_decomposition * Triangular_matrix

* Chapter 2 in the book “Numerical Recipes” : * 2.0 Introduction * 2.1 Gauss-Jordan Elimination
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f standard algorithms and //i.e.// quadratic time solutions using LU decomposition.</note> ===== Theory ====
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  • Dernière modification: 2020/10/02 14:58
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