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- methcalchim
- ====== Calculation methods applied to chemistry ====== ===== Synopsis (english) ===== ==== Mathematical prerequisites==== ==== Programming bases and to... orial with code execution * [[https://www.datacamp.com/courses/intro-to-python-for-data-science|DataCamp free course "Intro to Python for Data Science"]
- numerical_methods_for_ordinary_differential_equations
- fferential Equations]] (ODE, ODEs) * [[wp>Numerical_methods_for_ordinary_differential_equations|Numerical methods for ordinary differential equations]] * [[wp>Numerical_methods_for_ordinary_differential_equations#Eule... family is generally referred to as "RK4", "classical Runge–Kutta method" or simply as "the Runge–Kutt
- numerical_integration
- ====== Numerical integration ====== <note tip> Calculation of definite integrals implies to replace the function by a... d approximation and easier to compute. [[wp>Numerical_integration#Conservative_.28a_priori.29_error_es... e> * Equally spaced methods : * [[wp>Numerical_integration]] * [[wp>Trapezoidal_rule]]
- partial_differential_equation
- ====== Numerical solutions of PDE ====== <note warning>In general, the numerical solutions of partial differential equations are ... f variational principles. </note> * [[wp>Numerical_partial_differential_equations|Numerical partial differential equations]] However, the [[wp>Finite_
- system_of_linear_equations
- System of linear equations ====== <note tip>Numerical methods used to solve such problem allow to intr... k_substitution]] * Chapter 2 in the book "Numerical Recipes" : * 2.0 Introduction * 2.1 Gaus... stitution * 2.3 LU Decomposition and Its Application * Python [[https://docs.scipy.org/doc/numpy... linusable/libraries/samples-public/html/notebooks/calculation_methods_applied_to_chemistry/Gauss-Jorda
- root-finding_algorithm
- roots of an equation use iterations, and a numerical criterion to accept a solution when a sufficient... if f(a) and f(b) have opposite signs. * [[wp>Secant_method|Secant method]] (retains the last two computed points) * [[wp>False_position_method|Regula... Raphson method]] * Chapter 9 in the book "Numerical Recipes" : Root finding an nonlinear sets of equ
- eigenvalues_and_eigenvectors
- Power_iteration|Power iteration]], a simple numerical algorithm producing a number $\lambda$, the grea... * [[wp>QR_algorithm|QR algorithm]] ===== Applications ===== * collisional relaxation * //e.g... nction-eigenvalue expansion: Analysis of a simple case]] Wendell Forst, J. Chem. Educ., 1989, 66 (2), ... normal modes analysis (molecular vibrations) * PCA (principal component analysis) * Schrödinger eq