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- methcalchim
- opsis (english) ===== ==== Mathematical prerequisites==== ==== Programming bases and tools ==== * ... thon.org/|LearnPython.org]] interactive tutorial with code execution * [[https://www.datacamp.com/... Course/Python/|Python 3 Tutorial]], interactive, with [[https://code.sololearn.com/#py|code use in web... www.edx.org/course/introduction-computer-science-mitx-6-00-1x-9|Introduction to Computer Science and P
- system_of_linear_equations
- w to introduce and experiment on [[wp>Time_complexity]], considering cubic time behavior of standard algorithms and //i.e.// quadratic time solutions using LU decomposition.</note> ===== Theory ===== * [[wp>System_of... [wp>Pivot_element]], pivoting * [[wp>LU_decomposition]] * [[wp>Triangular_matrix#Forward_and_bac
- partial_differential_equation
- and implemented in specialized softwares : * Finite element method * Finite volume method * Boundary element method * Spectral method * Multigri... al differential equations]] However, the [[wp>Finite_difference_method|finite difference method]] can be more easliy applied to a lot of classical PDE. I
- numerical_methods_for_ordinary_differential_equations
- st|Pierre François Verhulst]] model and non-linearity * bifurcation, period doubling and routes to c... ifferential equations (the Lorenz equations, note it is not Lorentz) first studied by Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attracto
- eigenvalues_and_eigenvectors
- ctors]] * Important matrix properties * Hermitian, orthogonality,... * [[wp>Eigenvalue_algorithm|Eigenvalue algorithm]] * [[wp>Power_iteration|Power iteration]], a simple numerical algorithm p
- root-finding_algorithm
- ings : equations f(x) = 0 ====== <note tip> Algorithm used to find roots of an equation use iterations, and a numerical criterion to accept a solution when a sufficiently accurate value is reached... s_method|Bairstow's method]] is an efficient algorithm for finding the roots of a real polynomial of a
- numerical_integration
- integration ====== <note tip> Calculation of definite integrals implies to replace the function by ano... od and refinement of spatial grid discretization. It is interesting to check these errors using various algorithm and mesh resolution. </note> * Equally space... –Cotes_formulas]] * [[wp>Simpson's_rule#Composite_Simpson.27s_rule|Simpson's rule and composite Si