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- methcalchim
- matical prerequisites==== ==== Programming bases and tools ==== * Python programming language *... https://www.coursera.org/course/interactivepython|An Introduction to Interactive Programming in Python... e-mitx-6-00-1x-9|Introduction to Computer Science and Programming Using Python]] (edX) * [[wp>Anaconda_(Python_distribution)|Anaconda Python distributio
- eigenvalues_and_eigenvectors
- ====== Eigenvalues and eigenvectors ====== * [[wp>Eigenvalues_and_eigenvectors|Eigenvalues and eigenvectors]] * Important matrix properties * Hermitian, orthogo... t (in absolute value) eigenvalue of a matrix $A$, and the corresponding eigenvector $v$, such that $Av
- numerical_methods_for_ordinary_differential_equations
- mics, [[wp>Logistic_function|Logistic function]] (and equation) * [[wp>Pierre_François_Verhulst|Pierre François Verhulst]] model and non-linearity * bifurcation, period doubling and routes to chaos * Oscillating chemical reaction... ng chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz at
- root-finding_algorithm
- ===== <note tip> Algorithm used to find roots of an equation use iterations, and a numerical criterion to accept a solution when a sufficiently accurate ... he rate of convergence depends on the used method and the function f(x). Some methods (Newton-Raphson)... s : [[wp>Bairstow's_method|Bairstow's method]] is an efficient algorithm for finding the roots of a re
- partial_differential_equation
- tions are obtained by standard methods developped and implemented in specialized softwares : * Finit... epresented by their values at certain grid points and derivatives are approximated through differences... e of the most usual problems concern the chemical and thermal diffusion problem, in either steady and unsteady conditions, for which same equations apply.
- system_of_linear_equations
- ods used to solve such problem allow to introduce and experiment on [[wp>Time_complexity]], considering cubic time behavior of standard algorithms and //i.e.// quadratic time solutions using LU decom... quations]] * [[wp>Gaussian_elimination]], Gauss and Gauss-Jordan eliminations (diagonalization, tria... omposition]] * [[wp>Triangular_matrix#Forward_and_back_substitution]] * Chapter 2 in the book "N
- numerical_integration
- nite 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#Co... estimation]] depends on parameters of the method and refinement of spatial grid discretization. It is... ing to check these errors using various algorithm and mesh resolution. </note> * Equally spaced met