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Mathematics Subject Classification – MSC2010

65-XX

Numerical analysis 275410

65-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 128

65-01

Instructional exposition (textbooks, tutorial papers, etc.) 2084

65-02

Research exposition (monographs, survey articles) 2377

65-03

Historical (must also be assigned at least one classification number from Section 01) 476

65-04

Explicit machine computation and programs (not the theory of computation or programming) 814

65-05

Experimental papers 35

65-06

Proceedings, conferences, collections, etc. 3601

65Axx

Tables 492

65A05

Tables 480

65A99

None of the above, but in this section 11

65Bxx

Acceleration of convergence 2003

65B05

Extrapolation to the limit, deferred corrections 907

65B10

Summation of series 653

65B15

Euler-Maclaurin formula 295

65B99

None of the above, but in this section 244

65Cxx

Probabilistic methods, simulation and stochastic differential equations [For theoretical aspects, see 68U20 and 60H35] 39567

65C05

Monte Carlo methods 11921

65C10

Random number generation 2464

65C20

Models, numerical methods [See also 68U20] 4313

65C30

Stochastic differential and integral equations 2946

65C35

Stochastic particle methods [See also 82C80] 351

65C40

Computational Markov chains 2360

65C50

Other computational problems in probability 905

65C60

Computational problems in statistics 13165

65C99

None of the above, but in this section 5040

65Dxx

Numerical approximation and computational geometry (primarily algorithms) [For theory, see 41-XX and 68Uxx] 32166

65D05

Interpolation 5155

65D07

Splines 4947

65D10

Smoothing, curve fitting 3011

65D15

Algorithms for functional approximation 2537

65D17

Computer aided design (modeling of curves and surfaces) [See also 68U07] 4588

65D18

Computer graphics, image analysis, and computational geometry [See also 51N05, 68U05] 4550

65D19

Computational issues in computer and robotic vision 55

65D20

Computation of special functions, construction of tables [See also 33F05] 2512

65D25

Numerical differentiation 1460

65D30

Numerical integration 3308

65D32

Quadrature and cubature formulas 5196

65D99

None of the above, but in this section 507

65Exx

Numerical methods in complex analysis (potential theory, etc.) [For numerical methods in conformal mapping, see also 30C30] 1377

65E05

Numerical methods in complex analysis (potential theory, etc.) [For numerical methods in conformal mapping, see also 30C30] 1374

65E99

None of the above, but in this section 3

65Fxx

Numerical linear algebra 36084

65F05

Direct methods for linear systems and matrix inversion 5676

65F08

Preconditioners for iterative methods 1786

65F10

Iterative methods for linear systems [See also 65N22] 13391

65F15

Eigenvalues, eigenvectors 6664

65F18

Inverse eigenvalue problems 391

65F20

Overdetermined systems, pseudoinverses 3476

65F22

Ill-posedness, regularization 947

65F25

Orthogonalization 711

65F30

Other matrix algorithms 5890

65F35

Matrix norms, conditioning, scaling [See also 15A12, 15A60] 4576

65F40

Determinants 442

65F50

Sparse matrices 3571

65F60

Matrix exponential and similar matrix functions 234

65F99

None of the above, but in this section 567

65Gxx

Error analysis and interval analysis 5682

65G20

Algorithms with automatic result verification 414

65G30

Interval and finite arithmetic 2711

65G40

General methods in interval analysis 555

65G50

Roundoff error 1840

65G99

None of the above, but in this section 374

65Hxx

Nonlinear algebraic or transcendental equations 11841

65H04

Roots of polynomial equations 472

65H05

Single equations 4070

65H10

Systems of equations 6274

65H17

Eigenvalues, eigenvectors [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30] 540

65H20

Global methods, including homotopy approaches [See also 58C30, 90C30] 699

65H99

None of the above, but in this section 119

65Jxx

Numerical analysis in abstract spaces 11233

65J05

General theory 1649

65J08

Abstract evolution equations 158

65J10

Equations with linear operators (do not use 65Fxx) 2775

65J15

Equations with nonlinear operators (do not use 65Hxx) 4740

65J20

Improperly posed problems; regularization 1599

65J22

Inverse problems 614

65J99

None of the above, but in this section 1118

65Kxx

Mathematical programming, optimization and variational techniques 29180

65K05

Mathematical programming methods [See also 90Cxx] 18966

65K10

Optimization and variational techniques [See also 49Mxx, 93B40] 9517

65K15

Numerical methods for variational inequalities and related problems 865

65K99

None of the above, but in this section 174

65Lxx

Ordinary differential equations 27446

65L03

Functional-differential equations 375

65L04

Stiff equations 383

65L05

Initial value problems 11624

65L06

Multistep, Runge-Kutta and extrapolation methods 5375

65L07

Numerical investigation of stability of solutions 704

65L08

Improperly posed problems 63

65L09

Inverse problems 296

65L10

Boundary value problems 7032

65L11

Singularly perturbed problems 334

65L12

Finite difference methods 2250

65L15

Eigenvalue problems 1630

65L20

Stability and convergence of numerical methods 5205

65L50

Mesh generation and refinement 1367

65L60

Finite elements, Rayleigh-Ritz, Galerkin and collocation methods 2767

65L70

Error bounds 2122

65L80

Methods for differential-algebraic equations 821

65L99

None of the above, but in this section 1507

65Mxx

Partial differential equations, initial value and time-dependent initial-boundary value problems 40007

65M06

Finite difference methods 13852

65M08

Finite volume methods 1903

65M12

Stability and convergence of numerical methods 11483

65M15

Error bounds 5517

65M20

Method of lines 2893

65M22

Solution of discretized equations [See also 65Fxx, 65Hxx] 355

65M25

Method of characteristics 1050

65M30

Improperly posed problems 828

65M32

Inverse problems 1482

65M38

Boundary element methods 246

65M50

Mesh generation and refinement 2446

65M55

Multigrid methods; domain decomposition 1934

65M60

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 9572

65M70

Spectral, collocation and related methods 4401

65M75

Probabilistic methods, particle methods, etc. 598

65M80

Fundamental solutions, Green’s function methods, etc. 160

65M85

Fictitious domain methods 60

65M99

None of the above, but in this section 2680

65Nxx

Partial differential equations, boundary value problems 47576

65N06

Finite difference methods 6366

65N08

Finite volume methods 539

65N12

Stability and convergence of numerical methods 8211

65N15

Error bounds 7671

65N20

Ill-posed problems 237

65N21

Inverse problems 1311

65N22

Solution of discretized equations [See also 65Fxx, 65Hxx] 3686

65N25

Eigenvalue problems 2091

65N30

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 21657

65N35

Spectral, collocation and related methods 3573

65N38

Boundary element methods 3672

65N40

Method of lines 473

65N45

Method of contraction of the boundary 37

65N50

Mesh generation and refinement 4244

65N55

Multigrid methods; domain decomposition 5058

65N75

Probabilistic methods, particle methods, etc. 193

65N80

Fundamental solutions, Green’s function methods, etc. 397

65N85

Fictitious domain methods 64

65N99

None of the above, but in this section 2522

65Pxx

Numerical problems in dynamical systems [See also 37Mxx] 2646

65P10

Hamiltonian systems including symplectic integrators 1268

65P20

Numerical chaos 465

65P30

Bifurcation problems 473

65P40

Nonlinear stabilities 286

65P99

None of the above, but in this section 238

65Qxx

Difference and functional equations, recurrence relations 1442

65Q10

Difference equations 212

65Q20

Functional equations 54

65Q30

Recurrence relations 135

65Q99

None of the above, but in this section 7

65Rxx

Integral equations, integral transforms 14999

65R10

Integral transforms 2075

65R20

Integral equations 12371

65R30

Improperly posed problems 948

65R32

Inverse problems 569

65R99

None of the above, but in this section 94

65Sxx

Graphical methods 495

65S05

Graphical methods 495

65S99

None of the above, but in this section 0

65Txx

Numerical methods in Fourier analysis 9033

65T40

Trigonometric approximation and interpolation 1829

65T50

Discrete and fast Fourier transforms 2712

65T60

Wavelets 4499

65T99

None of the above, but in this section 229

65Yxx

Computer aspects of numerical algorithms 15461

65Y04

Algorithms for computer arithmetic, etc. [See also 68M07] 408

65Y05

Parallel computation 9143

65Y10

Algorithms for specific classes of architectures 1056

65Y15

Packaged methods 1497

65Y20

Complexity and performance of numerical algorithms [See also 68Q25] 3799

65Y99

None of the above, but in this section 517

65Zxx

Applications to physics 7689

65Z05

Applications to physics 7592

65Z99

None of the above, but in this section 98

Overview

General mathematics

History and biography

Mathematical logic and foundations

Combinatorics

Order, lattices, ordered algebraic structures

General algebraic systems

Number theory

Field theory and polynomials

Commutative algebra

Algebraic geometry

Linear and multilinear algebra; matrix theory

Associative rings and algebras

Nonassociative rings and algebras

Category theory, homological algebra

$K$-theory

Group theory and generalizations

Topological groups, Lie groups

Real functions

Measure and integration

Functions of a complex variable

Potential theory

Several complex variables and analytic spaces

Special functions

Ordinary differential equations

Partial differential equations

Dynamical systems and ergodic theory

Difference and functional equations

Sequences, series, summability

Approximation and expansions

Harmonic analysis on Euclidean spaces

Abstract harmonic analysis

Integral transforms, operational calculus

Integral equations

Functional analysis

Operator theory

Calculus of variations and optimal control; optimization

Geometry

Convex and discrete geometry

Differential geometry

General topology

Algebraic topology

Manifolds and cell complexes

Global analysis, analysis on manifolds

Probability theory and stochastic processes

Statistics

Numerical analysis

Computer science

Mechanics of particles and systems

Mechanics of deformable solids

Fluid mechanics

Optics, electromagnetic theory

Classical thermodynamics, heat transfer

Quantum Theory

Statistical mechanics, structure of matter

Relativity and gravitational theory

Astronomy and astrophysics

Geophysics

Operations research, mathematical programming

Game theory, economics, social and behavioral sciences

Biology and other natural sciences

Systems theory; control

Information and communication, circuits

Mathematics education

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cc	classification code
ct	classification text

a & b	logical and	abc*	right wildcard
a \| b	logical or	"ab c"	phrase
!ab	logical not	(ab c)	parentheses

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Mathematics Subject Classification – MSC2010

Overview