teaching:methcalchim:numerical_integration

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teaching:methcalchim:numerical_integration [2016/11/25 14:01] villersdteaching:methcalchim:numerical_integration [2018/10/09 07:59] (Version actuelle) villersd
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 ====== Numerical integration ====== ====== Numerical integration ======
-<note important+<note tip
-Calculation of definite integrals implies to replace the function by another one usually a polynomial form) which is a good approximation and easier to compute. 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 resolution.+Calculation of definite integrals implies to replace the function by another one (usually a polynomial form) which is a good approximation and easier to compute. [[wp>Numerical_integration#Conservative_.28a_priori.29_error_estimation|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 resolution.
 </note> </note>
  
   * Equally spaced methods :   * Equally spaced methods :
-    * [[wp>]Numerical_integration]]+    * [[wp>Numerical_integration]]
     * [[wp>Trapezoidal_rule]]     * [[wp>Trapezoidal_rule]]
     * [[wp>Newton–Cotes_formulas]]     * [[wp>Newton–Cotes_formulas]]
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   * If intervals between interpolation points vary :   * If intervals between interpolation points vary :
     * [[wp>Gaussian_quadrature]]     * [[wp>Gaussian_quadrature]]
 +  * Chapter 4 in the book “Numerical Recipes” : Integration of Functions
 +    * 4.0 Introduction
 +    * 4.1 Classical Formulas for Equally Spaced Abscissas
 +    * 4.2 Elementary Algorithms
 +    * 4.5 Gaussian Quadratures and Orthogonal Polynomials
 +  * Python SciPy library : [[https://docs.scipy.org/doc/scipy/reference/|SciPy Reference]]
 +    * [[https://docs.scipy.org/doc/scipy/reference/tutorial/integrate.html|Integration (scipy.integrate)]]
 +
 +===== Applications =====
 +  * Perform better integration calculus compare to [[https://pubs.acs.org/doi/10.1021/acs.jchemed.8b00193|Employing Spreadsheets for Applying Calculus in Upper-Level Chemistry Courses]] Paul D. Cooper, J. Chem. Educ., 2018, 95 (10), pp 1890–1893 DOI: 10.1021/acs.jchemed.8b00193
  
 ===== Références ===== ===== Références =====
   * Numerical recipes, The Art of Scientific Computing 3rd Edition, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, 2007, isbn: 9780521880688   * Numerical recipes, The Art of Scientific Computing 3rd Edition, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery, 2007, isbn: 9780521880688
     * [[http://numerical.recipes/]]     * [[http://numerical.recipes/]]
 +      * in C : [[http://apps.nrbook.com/c/index.html]]
     * [[http://www2.units.it/ipl/students_area/imm2/files/Numerical_Recipes.pdf]], p 129...     * [[http://www2.units.it/ipl/students_area/imm2/files/Numerical_Recipes.pdf]], p 129...
     * [[http://apps.nrbook.com/empanel/index.html#]]     * [[http://apps.nrbook.com/empanel/index.html#]]
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