مستخدم:Chaos/قائمة مواضيع التحليل العددي

Euler integration — the most basic method for solving an ODE
Runge-Kutta methods — one of the two main classes of methods for initial value problems
- Midpoint method — a second-order method with two stages
Multistep method — the other main class of methods for initial value problems
Newmark-beta method — a method specifically designed for the solution of problems from classical physics
Verlet integration — another method for problems from classical physics
Geometric integrator — a method that preserves some geometric structure of the equation
- Symplectic integrator — a method for the solution of Hamilton's equations that preserves the symplectic structure
Stiff equation — roughly, an ODE for which the unstable methods needs a very short step size, but stable methods do not.
Shooting method — a method for the solution of boundary value problems
- Illustration of the shooting method

معادلات تفاضلية جزئية عددية عدل

Numerical partial differential equations — the numerical solution of partial differential equations (PDEs)

Methods for the solution of PDEs:
- Finite difference method — based on approximating differential operators with difference operators
  - Discrete Laplace operator — finite-difference approximation of the Laplace operator
  - Crank-Nicolson method — second-order method for heat and related PDEs
- Finite element method, finite element analysis — based on a discretization of the space of solutions
  - Galerkin method — a finite element method in which the residual is orthogonal to the finite element space
  - Rayleigh-Ritz method — a finite element method based on variational principles
  - Direct stiffness method — a particular implementation of the finite element method, often used in structural analysis
- Spectral method — based on the Fourier transformation
  - Pseudo-spectral method
- Boundary element method — based on transforming the PDE to an integral equation on the boundary of the domain
- Analytic element method — similar to the boundary element method, but the integral equation is evaluated analytically
- Finite volume method — based on dividing the domain in many small domains; popular in computational fluid dynamics
- Discrete element method — a method in which the elements can move freely relative to each other
Techniques for improving these methods:
- Multigrid, multigrid method — uses a hierarchy of nested meshes to speed up the methods
- Domain decomposition method — divides the domain in a few subdomains and solves the PDE on these subdomains
- Adaptive mesh refinement — uses the computed solution to refine the mesh only where necessary
Mimetic methods — methods that respect in some sense the structure of the original problem
Numerical diffusion — diffusion introduced by the numerical method, above to that which is naturally present
Numerical resistivity — the same, with resistivity instead of diffusion
Multiphysics — models consisting of various submodels with different physics

طريقة مونتي كارلو عدل

متغيرات طريقة مونتي كارلو:
Box-Muller transform
Low-discrepancy sequence
- Constructions of low-discrepancy sequences
- Illustration of a low-discrepancy sequence
Parallel tempering
Techniques for reducing the variance:
تطبيقات:
Also see the list of statistics topics

تطبيقات عدل

برمجيات عدل

See also: List of numerical analysis software
Libraries:
لغات برمجة :
برامج :
- MATLAB
- GNU Octave
- Scilab
- Rlab
- TK Solver

مقالات تتطلب تصنيف عدل

Courant–Friedrichs–Lewy condition -- Explicit and implicit methods -- Finite element method in structural mechanics -- MISER algorithm -- Newton fractal -- Pseudospectrum -- Uniform theory of diffraction -- Weak formulation -- Radial basis function -- OpenBUGS -- Particle filter -- Braess' paradox -- Convex analysis -- Corner solution -- Discrete optimization -- Goal programming -- Pareto analysis -- Pareto principle -- Partial evaluation -- Subderivative -- Trust region -- Utility maximization problem -- Branch and bound -- Cutting-plane method -- Delayed column generation -- Karmarkar's algorithm -- MTD-f -- Reactive search -- Effective fitness -- Evolution strategy -- Evolutionary art -- Gene expression programming -- Human-based genetic algorithm -- Interactive evolutionary computation -- Interactive genetic algorithm -- Learning classifier system -- Memetic algorithm -- Neuroevolution -- Bairstow's method -- Durand-Kerner method -- Splitting circle method --

Complex wavelet transform / Discrete wavelet transform
Greedy algorithm, Greedy randomized adaptive search procedure, Hill climbing, Local search (optimization), Random-restart hill climbing (currently more about discrete optimization, but may be expanded to cover continuous optimization)
MANIAC II (computer)
Operations research (what is the relation between OR and optimization?)
Secular equation / Secular function
Structural analysis (very applied)

Category:Numerical analysis
Category:Approximation theory
Category:FFT algorithms
Category:Interpolation
Category:Monte Carlo method
Category:Numerical software is excluded, because it is covered by List of numerical analysis software
Category:Numerical linear algebra
Category:Optimization
- Category:Optimization algorithms
  - Category:Evolutionary algorithms
Category:Root-finding algorithms
Category:Splines

Category:Numerical software -- Category:Optimization software -- Category:Combinatorial optimization -- Category:Genetic algorithms -- Category:Genetic programming -- Category:Interactive evolutionary computation

[[:تصنيف:تحليل عددي|*]] [[:تصنيف:قوائم رياضية]]