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Mathematics Subject Classification – MSC2010

65-XX

Numerical analysis 280755

65-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 130

65-01

Instructional exposition (textbooks, tutorial papers, etc.) 2106

65-02

Research exposition (monographs, survey articles) 2410

65-03

Historical (must also be assigned at least one classification number from Section 01) 482

65-04

Explicit machine computation and programs (not the theory of computation or programming) 823

65-05

Experimental papers 36

65-06

Proceedings, conferences, collections, etc. 3612

65Axx

Tables 499

65A05

Tables 486

65A99

None of the above, but in this section 11

65Bxx

Acceleration of convergence 2020

65B05

Extrapolation to the limit, deferred corrections 914

65B10

Summation of series 658

65B15

Euler-Maclaurin formula 297

65B99

None of the above, but in this section 249

65Cxx

Probabilistic methods, simulation and stochastic differential equations [For theoretical aspects, see 68U20 and 60H35] 39871

65C05

Monte Carlo methods 12093

65C10

Random number generation 2473

65C20

Models, numerical methods [See also 68U20] 4318

65C30

Stochastic differential and integral equations 2996

65C35

Stochastic particle methods [See also 82C80] 354

65C40

Computational Markov chains 2383

65C50

Other computational problems in probability 913

65C60

Computational problems in statistics 13214

65C99

None of the above, but in this section 5045

65Dxx

Numerical approximation and computational geometry (primarily algorithms) [For theory, see 41-XX and 68Uxx] 32505

65D05

Interpolation 5235

65D07

Splines 5030

65D10

Smoothing, curve fitting 3042

65D15

Algorithms for functional approximation 2560

65D17

Computer aided design (modeling of curves and surfaces) [See also 68U07] 4640

65D18

Computer graphics, image analysis, and computational geometry [See also 51N05, 68U05] 4562

65D19

Computational issues in computer and robotic vision 60

65D20

Computation of special functions, construction of tables [See also 33F05] 2526

65D25

Numerical differentiation 1477

65D30

Numerical integration 3353

65D32

Quadrature and cubature formulas 5229

65D99

None of the above, but in this section 525

65Exx

Numerical methods in complex analysis (potential theory, etc.) [For numerical methods in conformal mapping, see also 30C30] 1382

65E05

Numerical methods in complex analysis (potential theory, etc.) [For numerical methods in conformal mapping, see also 30C30] 1379

65E99

None of the above, but in this section 3

65Fxx

Numerical linear algebra 36633

65F05

Direct methods for linear systems and matrix inversion 5722

65F08

Preconditioners for iterative methods 1862

65F10

Iterative methods for linear systems [See also 65N22] 13589

65F15

Eigenvalues, eigenvectors 6772

65F18

Inverse eigenvalue problems 400

65F20

Overdetermined systems, pseudoinverses 3494

65F22

Ill-posedness, regularization 987

65F25

Orthogonalization 719

65F30

Other matrix algorithms 5986

65F35

Matrix norms, conditioning, scaling [See also 15A12, 15A60] 4600

65F40

Determinants 448

65F50

Sparse matrices 3628

65F60

Matrix exponential and similar matrix functions 250

65F99

None of the above, but in this section 579

65Gxx

Error analysis and interval analysis 5743

65G20

Algorithms with automatic result verification 423

65G30

Interval and finite arithmetic 2727

65G40

General methods in interval analysis 568

65G50

Roundoff error 1849

65G99

None of the above, but in this section 391

65Hxx

Nonlinear algebraic or transcendental equations 11975

65H04

Roots of polynomial equations 486

65H05

Single equations 4094

65H10

Systems of equations 6356

65H17

Eigenvalues, eigenvectors [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30] 548

65H20

Global methods, including homotopy approaches [See also 58C30, 90C30] 705

65H99

None of the above, but in this section 121

65Jxx

Numerical analysis in abstract spaces 11358

65J05

General theory 1655

65J08

Abstract evolution equations 163

65J10

Equations with linear operators (do not use 65Fxx) 2789

65J15

Equations with nonlinear operators (do not use 65Hxx) 4805

65J20

Improperly posed problems; regularization 1618

65J22

Inverse problems 639

65J99

None of the above, but in this section 1119

65Kxx

Mathematical programming, optimization and variational techniques 29613

65K05

Mathematical programming methods [See also 90Cxx] 19185

65K10

Optimization and variational techniques [See also 49Mxx, 93B40] 9695

65K15

Numerical methods for variational inequalities and related problems 900

65K99

None of the above, but in this section 178

65Lxx

Ordinary differential equations 27825

65L03

Functional-differential equations 386

65L04

Stiff equations 399

65L05

Initial value problems 11721

65L06

Multistep, Runge-Kutta and extrapolation methods 5445

65L07

Numerical investigation of stability of solutions 716

65L08

Improperly posed problems 63

65L09

Inverse problems 304

65L10

Boundary value problems 7089

65L11

Singularly perturbed problems 344

65L12

Finite difference methods 2285

65L15

Eigenvalue problems 1637

65L20

Stability and convergence of numerical methods 5249

65L50

Mesh generation and refinement 1376

65L60

Finite elements, Rayleigh-Ritz, Galerkin and collocation methods 2835

65L70

Error bounds 2134

65L80

Methods for differential-algebraic equations 838

65L99

None of the above, but in this section 1548

65Mxx

Partial differential equations, initial value and time-dependent initial-boundary value problems 40936

65M06

Finite difference methods 14142

65M08

Finite volume methods 1991

65M12

Stability and convergence of numerical methods 11713

65M15

Error bounds 5616

65M20

Method of lines 2926

65M22

Solution of discretized equations [See also 65Fxx, 65Hxx] 382

65M25

Method of characteristics 1059

65M30

Improperly posed problems 840

65M32

Inverse problems 1522

65M38

Boundary element methods 258

65M50

Mesh generation and refinement 2483

65M55

Multigrid methods; domain decomposition 1970

65M60

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 9817

65M70

Spectral, collocation and related methods 4519

65M75

Probabilistic methods, particle methods, etc. 631

65M80

Fundamental solutions, Green’s function methods, etc. 166

65M85

Fictitious domain methods 62

65M99

None of the above, but in this section 2731

65Nxx

Partial differential equations, boundary value problems 48384

65N06

Finite difference methods 6424

65N08

Finite volume methods 564

65N12

Stability and convergence of numerical methods 8351

65N15

Error bounds 7827

65N20

Ill-posed problems 252

65N21

Inverse problems 1360

65N22

Solution of discretized equations [See also 65Fxx, 65Hxx] 3719

65N25

Eigenvalue problems 2133

65N30

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 22120

65N35

Spectral, collocation and related methods 3648

65N38

Boundary element methods 3709

65N40

Method of lines 478

65N45

Method of contraction of the boundary 38

65N50

Mesh generation and refinement 4302

65N55

Multigrid methods; domain decomposition 5121

65N75

Probabilistic methods, particle methods, etc. 201

65N80

Fundamental solutions, Green’s function methods, etc. 413

65N85

Fictitious domain methods 69

65N99

None of the above, but in this section 2542

65Pxx

Numerical problems in dynamical systems [See also 37Mxx] 2700

65P10

Hamiltonian systems including symplectic integrators 1292

65P20

Numerical chaos 471

65P30

Bifurcation problems 480

65P40

Nonlinear stabilities 296

65P99

None of the above, but in this section 245

65Qxx

Difference and functional equations, recurrence relations 1454

65Q10

Difference equations 217

65Q20

Functional equations 58

65Q30

Recurrence relations 143

65Q99

None of the above, but in this section 7

65Rxx

Integral equations, integral transforms 15144

65R10

Integral transforms 2092

65R20

Integral equations 12482

65R30

Improperly posed problems 955

65R32

Inverse problems 584

65R99

None of the above, but in this section 92

65Sxx

Graphical methods 494

65S05

Graphical methods 494

65S99

None of the above, but in this section 0

65Txx

Numerical methods in Fourier analysis 9202

65T40

Trigonometric approximation and interpolation 1835

65T50

Discrete and fast Fourier transforms 2776

65T60

Wavelets 4597

65T99

None of the above, but in this section 232

65Yxx

Computer aspects of numerical algorithms 15705

65Y04

Algorithms for computer arithmetic, etc. [See also 68M07] 430

65Y05

Parallel computation 9289

65Y10

Algorithms for specific classes of architectures 1079

65Y15

Packaged methods 1515

65Y20

Complexity and performance of numerical algorithms [See also 68Q25] 3839

65Y99

None of the above, but in this section 521

65Zxx

Applications to physics 7737

65Z05

Applications to physics 7631

65Z99

None of the above, but in this section 103

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