65-XX Numerical analysis
65-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
65-01 Instructional exposition (textbooks, tutorial papers, etc.)
65-02 Research exposition (monographs, survey articles)
65-03 Historical {!must also be assigned at least one classification number from section 01}
65-04 Explicit machine computation and programs (not the theory of computation or programming)
65-05 Experimental papers
65-06 Proceedings, conferences, collections, etc.
65A05 Tables
65Bxx Acceleration of convergence
65B05 Extrapolation to the limit, deferred corrections
65B10 Summation of series
65B15 Euler - Maclaurin formula
65B99 None of the above, but in this section
65Cxx Probabilistic methods, simulation and stochastic differential equations {For theoretical aspects, see 68U20 and 60H35}
65C05 Monte_Carlo methods
65C10 Random number generation
65C20 Models, numerical methods [See also 68U20]
65C30 Stochastic differential and integral equations
65C35 Stochastic particle methods [See also 82C80]
65C40 Computational Markov chains
65C50 Other computational problems in probability
65C60 Computational problems in statistics
65C99 None of the above, but in this section
65Dxx Numerical approximation and computational geometry (primarily algorithms) {For theory, see 41-XX and 68Uxx}
65D05 Interpolation
65D07 Splines
65D10 Smoothing, curve fitting
65D15 Algorithms for functional approximation
65D17 Computer aided design (modeling of curves and surfaces) [See also 68U07]
65D18 Computer graphics and computational geometry [See also 51N05, 68U05]
65D20 Computation of special functions, construction of tables [See also 33F05]
65D25 Numerical differentiation
65D30 Numerical integration
65D32 Quadrature and cubature formulas
65D99 None of the above, but in this section
65E05 Numerical methods in complex analysis (potential theory, etc.) {For numerical methods in conformal mapping, see 30C30}
65Fxx Numerical linear algebra
65F05 Direct methods for linear systems and matrix inversion
65F10 Iterative methods for linear systems [See also 65N22]
65F15 Eigenvalues, eigenvectors
65F18 Inverse eigenvalue problems
65F20 Overdetermined systems, pseudoinverses
65F22 Ill-posedness, regularization
65F25 Orthogonalization
65F30 Other matrix algorithms
65F35 Matrix norms, conditioning, scaling [See also 15A12, 15A60]
65F40 Determinants
65F50 Sparse matrices
65F99 None of the above, but in this section
65Gxx Error analysis and interval analysis
65G20 Algorithm with automatic result verification
65G30 Interval and finite arithmetic
65G40 General methods in interval analysis
65G50 Roundoff error
65G99 None of the above, but in this section
65Hxx Nonlinear algebraic or transcendental equations
65H05 Single equations
65H10 Systems of equations
65H17 Eigenvalues, eigenvectors [See also 58C40, 58E07, 47Hxx, 47Jxx, 90C30]
65H20 Global methods, including homotopy approaches [See also 58C30, 90C30]
65H99 None of the above, but in this section
65Jxx Numerical analysis in abstract spaces
65J05 General theory
65J10 Equations with linear operators {!do not use 65Fxx}
65J15 Equations with nonlinear operators {!do not use 65Hxx}
65J20 Improperly posed problems; regularization
65J22 Inverse problems
65J99 None of the above, but in this section
65Kxx Mathematical programming, optimization and variational techniques
65K05 Mathematical programming (algorithms) {For theory, see 90Cxx}
65K10 Optimization and variational techniques [See also 49Mxx, 93B40]
65K99 None of the above, but in this section
65Lxx Ordinary differential equations
65L05 Initial value problems
65L06 Multistep, Runge - Kutta and extrapolation methods
65L07 Numerical investigation of stability of solutions
65L08 Improperly posed problems
65L09 Inverse problems
65L10 Boundary value problems
65L12 Finite difference methods
65L15 Eigenvalue problems
65L20 Stability and convergence of numerical methods
65L50 Mesh generation and refinement
65L60 Finite elements, Rayleigh - Ritz, Galerkin and collocation methods
65L70 Error bounds
65L80 Methods for differential-algebraic equations
65L99 None of the above, but in this section
65Mxx Partial differential equations, initial value and time-dependent initial-boundary value problems
65M06 Finite difference methods
65M12 Stability and convergence of numerical methods
65M15 Error bounds
65M20 Method of lines
65M25 Method of characteristics
65M30 Improperly posed problems
65M32 Inverse problems
65M50 Mesh generation and refinement
65M55 Multigrid methods; domain decomposition
65M60 Finite elements, Rayleigh - Ritz and Galerkin methods, finite methods
65M70 Spectral, collocation and related methods
65M99 None of the above, but in this section
65Nxx Partial differential equations, boundary value problems
65N06 Finite difference methods
65N12 Stability and convergence of numerical methods
65N15 Error bounds
65N21 Inverse problems
65N22 Solution of discretized equations [See also 65Fxx, 65Hxx]
65N25 Eigenvalue problems
65N30 Finite elements, Rayleigh - Ritz and Galerkin methods, finite methods
65N35 Spectral, collocation and related methods
65N38 Boundary element methods
65N40 Method of lines
65N45 Method of contraction of the boundary
65N50 Mesh generation and refinement
65N55 Multigrid methods; domain decomposition
65N99 None of the above, but in this section
65Pxx Numerical problems in dynamical systems [See also 37Mxx]
65P10 Hamiltonian systems including symplectic integrators
65P20 Numerical chaos
65P30 Bifurcation problems
65P40 Nonlinear stabilities
65P99 None of the above, but in this section
65Q05 Difference and functional equations, recurrence relations
65Rxx Integral equations, integral transforms
65R10 Integral transforms
65R20 Integral equations
65R30 Improperly posed problems
65R32 Inverse problems
65R99 None of the above but in this section
65S05 Graphical methods
65Txx Numerical methods in Fourier analysis
65T40 Trigonometric approximation and interpolation
65T50 Discrete and fast Fourier transforms
65T60 Wavelets
65T99 None of the above, but in this section
65Yxx Computer aspects of numerical algorithms
65Y05 Parallel computation
65Y10 Algorithms for specific classes of architectures
65Y15 Packaged methods
65Y20 Complexity and performance of numerical algorithms [See also 68Q25]
65Y99 None of the above, but in this section
65Z05 Applications to physics