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Mathematics Subject Classification – MSC2010

65-XX

Numerical analysis 284968

65-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 132

65-01

Instructional exposition (textbooks, tutorial papers, etc.) 2123

65-02

Research exposition (monographs, survey articles) 2426

65-03

Historical (must also be assigned at least one classification number from Section 01) 492

65-04

Explicit machine computation and programs (not the theory of computation or programming) 825

65-05

Experimental papers 36

65-06

Proceedings, conferences, collections, etc. 3642

65Axx

Tables 501

65A05

Tables 485

65A99

None of the above, but in this section 11

65Bxx

Acceleration of convergence 2046

65B05

Extrapolation to the limit, deferred corrections 924

65B10

Summation of series 663

65B15

Euler-Maclaurin formula 299

65B99

None of the above, but in this section 259

65Cxx

Probabilistic methods, simulation and stochastic differential equations [For theoretical aspects, see 68U20 and 60H35] 40158

65C05

Monte Carlo methods 12250

65C10

Random number generation 2487

65C20

Models, numerical methods [See also 68U20] 4335

65C30

Stochastic differential and integral equations 3065

65C35

Stochastic particle methods [See also 82C80] 353

65C40

Computational Markov chains 2401

65C50

Other computational problems in probability 921

65C60

Computational problems in statistics 13250

65C99

None of the above, but in this section 5049

65Dxx

Numerical approximation and computational geometry (primarily algorithms) [For theory, see 41-XX and 68Uxx] 33039

65D05

Interpolation 5297

65D07

Splines 5131

65D10

Smoothing, curve fitting 3060

65D15

Algorithms for functional approximation 2586

65D17

Computer aided design (modeling of curves and surfaces) [See also 68U07] 4682

65D18

Computer graphics, image analysis, and computational geometry [See also 51N05, 68U05] 4587

65D19

Computational issues in computer and robotic vision 61

65D20

Computation of special functions, construction of tables [See also 33F05] 2531

65D25

Numerical differentiation 1491

65D30

Numerical integration 3424

65D32

Quadrature and cubature formulas 5287

65D99

None of the above, but in this section 531

65Exx

Numerical methods in complex analysis (potential theory, etc.) [For numerical methods in conformal mapping, see also 30C30] 1397

65E05

Numerical methods in complex analysis (potential theory, etc.) [For numerical methods in conformal mapping, see also 30C30] 1392

65E99

None of the above, but in this section 4

65Fxx

Numerical linear algebra 37009

65F05

Direct methods for linear systems and matrix inversion 5763

65F08

Preconditioners for iterative methods 1935

65F10

Iterative methods for linear systems [See also 65N22] 13733

65F15

Eigenvalues, eigenvectors 6848

65F18

Inverse eigenvalue problems 405

65F20

Overdetermined systems, pseudoinverses 3510

65F22

Ill-posedness, regularization 1002

65F25

Orthogonalization 727

65F30

Other matrix algorithms 6058

65F35

Matrix norms, conditioning, scaling [See also 15A12, 15A60] 4634

65F40

Determinants 452

65F50

Sparse matrices 3685

65F60

Matrix exponential and similar matrix functions 271

65F99

None of the above, but in this section 586

65Gxx

Error analysis and interval analysis 5789

65G20

Algorithms with automatic result verification 432

65G30

Interval and finite arithmetic 2738

65G40

General methods in interval analysis 580

65G50

Roundoff error 1854

65G99

None of the above, but in this section 402

65Hxx

Nonlinear algebraic or transcendental equations 12108

65H04

Roots of polynomial equations 492

65H05

Single equations 4138

65H10

Systems of equations 6423

65H17

Eigenvalues, eigenvectors [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30] 551

65H20

Global methods, including homotopy approaches [See also 58C30, 90C30] 716

65H99

None of the above, but in this section 125

65Jxx

Numerical analysis in abstract spaces 11451

65J05

General theory 1659

65J08

Abstract evolution equations 170

65J10

Equations with linear operators (do not use 65Fxx) 2803

65J15

Equations with nonlinear operators (do not use 65Hxx) 4840

65J20

Improperly posed problems; regularization 1639

65J22

Inverse problems 658

65J99

None of the above, but in this section 1120

65Kxx

Mathematical programming, optimization and variational techniques 29876

65K05

Mathematical programming methods [See also 90Cxx] 19330

65K10

Optimization and variational techniques [See also 49Mxx, 93B40] 9795

65K15

Numerical methods for variational inequalities and related problems 930

65K99

None of the above, but in this section 178

65Lxx

Ordinary differential equations 28207

65L03

Functional-differential equations 411

65L04

Stiff equations 412

65L05

Initial value problems 11824

65L06

Multistep, Runge-Kutta and extrapolation methods 5554

65L07

Numerical investigation of stability of solutions 728

65L08

Improperly posed problems 64

65L09

Inverse problems 310

65L10

Boundary value problems 7140

65L11

Singularly perturbed problems 361

65L12

Finite difference methods 2328

65L15

Eigenvalue problems 1648

65L20

Stability and convergence of numerical methods 5308

65L50

Mesh generation and refinement 1382

65L60

Finite elements, Rayleigh-Ritz, Galerkin and collocation methods 2901

65L70

Error bounds 2146

65L80

Methods for differential-algebraic equations 844

65L99

None of the above, but in this section 1569

65Mxx

Partial differential equations, initial value and time-dependent initial-boundary value problems 42118

65M06

Finite difference methods 14521

65M08

Finite volume methods 2095

65M12

Stability and convergence of numerical methods 12004

65M15

Error bounds 5760

65M20

Method of lines 2963

65M22

Solution of discretized equations [See also 65Fxx, 65Hxx] 414

65M25

Method of characteristics 1081

65M30

Improperly posed problems 844

65M32

Inverse problems 1573

65M38

Boundary element methods 309

65M50

Mesh generation and refinement 2517

65M55

Multigrid methods; domain decomposition 1998

65M60

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 10144

65M70

Spectral, collocation and related methods 4704

65M75

Probabilistic methods, particle methods, etc. 697

65M80

Fundamental solutions, Green’s function methods, etc. 178

65M85

Fictitious domain methods 65

65M99

None of the above, but in this section 2784

65Nxx

Partial differential equations, boundary value problems 49540

65N06

Finite difference methods 6508

65N08

Finite volume methods 584

65N12

Stability and convergence of numerical methods 8477

65N15

Error bounds 7961

65N20

Ill-posed problems 263

65N21

Inverse problems 1418

65N22

Solution of discretized equations [See also 65Fxx, 65Hxx] 3748

65N25

Eigenvalue problems 2171

65N30

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 22544

65N35

Spectral, collocation and related methods 3786

65N38

Boundary element methods 4048

65N40

Method of lines 478

65N45

Method of contraction of the boundary 38

65N50

Mesh generation and refinement 4346

65N55

Multigrid methods; domain decomposition 5178

65N75

Probabilistic methods, particle methods, etc. 214

65N80

Fundamental solutions, Green’s function methods, etc. 483

65N85

Fictitious domain methods 76

65N99

None of the above, but in this section 2563

65Pxx

Numerical problems in dynamical systems [See also 37Mxx] 2745

65P10

Hamiltonian systems including symplectic integrators 1315

65P20

Numerical chaos 481

65P30

Bifurcation problems 486

65P40

Nonlinear stabilities 304

65P99

None of the above, but in this section 248

65Qxx

Difference and functional equations, recurrence relations 1473

65Q10

Difference equations 226

65Q20

Functional equations 59

65Q30

Recurrence relations 156

65Q99

None of the above, but in this section 6

65Rxx

Integral equations, integral transforms 15296

65R10

Integral transforms 2106

65R20

Integral equations 12615

65R30

Improperly posed problems 957

65R32

Inverse problems 592

65R99

None of the above, but in this section 94

65Sxx

Graphical methods 499

65S05

Graphical methods 499

65S99

None of the above, but in this section 0

65Txx

Numerical methods in Fourier analysis 9345

65T40

Trigonometric approximation and interpolation 1841

65T50

Discrete and fast Fourier transforms 2820

65T60

Wavelets 4686

65T99

None of the above, but in this section 236

65Yxx

Computer aspects of numerical algorithms 15805

65Y04

Algorithms for computer arithmetic, etc. [See also 68M07] 434

65Y05

Parallel computation 9347

65Y10

Algorithms for specific classes of architectures 1093

65Y15

Packaged methods 1523

65Y20

Complexity and performance of numerical algorithms [See also 68Q25] 3880

65Y99

None of the above, but in this section 523

65Zxx

Applications to physics 7765

65Z05

Applications to physics 7661

65Z99

None of the above, but in this section 104

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
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Mathematics Subject Classification – MSC2010

Overview