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Mathematics Subject Classification – MSC2010

65-XX

Numerical analysis 277794

65-00

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

65-01

Instructional exposition (textbooks, tutorial papers, etc.) 2093

65-02

Research exposition (monographs, survey articles) 2386

65-03

Historical (must also be assigned at least one classification number from Section 01) 480

65-04

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

65-05

Experimental papers 35

65-06

Proceedings, conferences, collections, etc. 3594

65Axx

Tables 496

65A05

Tables 484

65A99

None of the above, but in this section 11

65Bxx

Acceleration of convergence 2011

65B05

Extrapolation to the limit, deferred corrections 911

65B10

Summation of series 656

65B15

Euler-Maclaurin formula 296

65B99

None of the above, but in this section 246

65Cxx

Probabilistic methods, simulation and stochastic differential equations [For theoretical aspects, see 68U20 and 60H35] 39669

65C05

Monte Carlo methods 11990

65C10

Random number generation 2464

65C20

Models, numerical methods [See also 68U20] 4313

65C30

Stochastic differential and integral equations 2956

65C35

Stochastic particle methods [See also 82C80] 353

65C40

Computational Markov chains 2367

65C50

Other computational problems in probability 906

65C60

Computational problems in statistics 13180

65C99

None of the above, but in this section 5043

65Dxx

Numerical approximation and computational geometry (primarily algorithms) [For theory, see 41-XX and 68Uxx] 32297

65D05

Interpolation 5185

65D07

Splines 4988

65D10

Smoothing, curve fitting 3024

65D15

Algorithms for functional approximation 2550

65D17

Computer aided design (modeling of curves and surfaces) [See also 68U07] 4601

65D18

Computer graphics, image analysis, and computational geometry [See also 51N05, 68U05] 4538

65D19

Computational issues in computer and robotic vision 57

65D20

Computation of special functions, construction of tables [See also 33F05] 2518

65D25

Numerical differentiation 1464

65D30

Numerical integration 3329

65D32

Quadrature and cubature formulas 5211

65D99

None of the above, but in this section 516

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 36300

65F05

Direct methods for linear systems and matrix inversion 5693

65F08

Preconditioners for iterative methods 1818

65F10

Iterative methods for linear systems [See also 65N22] 13467

65F15

Eigenvalues, eigenvectors 6717

65F18

Inverse eigenvalue problems 394

65F20

Overdetermined systems, pseudoinverses 3490

65F22

Ill-posedness, regularization 963

65F25

Orthogonalization 715

65F30

Other matrix algorithms 5925

65F35

Matrix norms, conditioning, scaling [See also 15A12, 15A60] 4585

65F40

Determinants 445

65F50

Sparse matrices 3598

65F60

Matrix exponential and similar matrix functions 240

65F99

None of the above, but in this section 569

65Gxx

Error analysis and interval analysis 5712

65G20

Algorithms with automatic result verification 418

65G30

Interval and finite arithmetic 2718

65G40

General methods in interval analysis 560

65G50

Roundoff error 1844

65G99

None of the above, but in this section 385

65Hxx

Nonlinear algebraic or transcendental equations 11906

65H04

Roots of polynomial equations 480

65H05

Single equations 4082

65H10

Systems of equations 6314

65H17

Eigenvalues, eigenvectors [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30] 545

65H20

Global methods, including homotopy approaches [See also 58C30, 90C30] 700

65H99

None of the above, but in this section 120

65Jxx

Numerical analysis in abstract spaces 11293

65J05

General theory 1650

65J08

Abstract evolution equations 161

65J10

Equations with linear operators (do not use 65Fxx) 2785

65J15

Equations with nonlinear operators (do not use 65Hxx) 4771

65J20

Improperly posed problems; regularization 1606

65J22

Inverse problems 627

65J99

None of the above, but in this section 1118

65Kxx

Mathematical programming, optimization and variational techniques 29355

65K05

Mathematical programming methods [See also 90Cxx] 19056

65K10

Optimization and variational techniques [See also 49Mxx, 93B40] 9596

65K15

Numerical methods for variational inequalities and related problems 876

65K99

None of the above, but in this section 177

65Lxx

Ordinary differential equations 27586

65L03

Functional-differential equations 377

65L04

Stiff equations 390

65L05

Initial value problems 11662

65L06

Multistep, Runge-Kutta and extrapolation methods 5399

65L07

Numerical investigation of stability of solutions 712

65L08

Improperly posed problems 63

65L09

Inverse problems 302

65L10

Boundary value problems 7048

65L11

Singularly perturbed problems 340

65L12

Finite difference methods 2261

65L15

Eigenvalue problems 1631

65L20

Stability and convergence of numerical methods 5218

65L50

Mesh generation and refinement 1369

65L60

Finite elements, Rayleigh-Ritz, Galerkin and collocation methods 2787

65L70

Error bounds 2127

65L80

Methods for differential-algebraic equations 822

65L99

None of the above, but in this section 1532

65Mxx

Partial differential equations, initial value and time-dependent initial-boundary value problems 40423

65M06

Finite difference methods 13979

65M08

Finite volume methods 1937

65M12

Stability and convergence of numerical methods 11576

65M15

Error bounds 5553

65M20

Method of lines 2908

65M22

Solution of discretized equations [See also 65Fxx, 65Hxx] 364

65M25

Method of characteristics 1053

65M30

Improperly posed problems 830

65M32

Inverse problems 1502

65M38

Boundary element methods 252

65M50

Mesh generation and refinement 2466

65M55

Multigrid methods; domain decomposition 1950

65M60

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 9683

65M70

Spectral, collocation and related methods 4459

65M75

Probabilistic methods, particle methods, etc. 614

65M80

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

65M85

Fictitious domain methods 61

65M99

None of the above, but in this section 2706

65Nxx

Partial differential equations, boundary value problems 47913

65N06

Finite difference methods 6392

65N08

Finite volume methods 554

65N12

Stability and convergence of numerical methods 8272

65N15

Error bounds 7733

65N20

Ill-posed problems 245

65N21

Inverse problems 1333

65N22

Solution of discretized equations [See also 65Fxx, 65Hxx] 3703

65N25

Eigenvalue problems 2108

65N30

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 21850

65N35

Spectral, collocation and related methods 3612

65N38

Boundary element methods 3687

65N40

Method of lines 477

65N45

Method of contraction of the boundary 38

65N50

Mesh generation and refinement 4264

65N55

Multigrid methods; domain decomposition 5087

65N75

Probabilistic methods, particle methods, etc. 197

65N80

Fundamental solutions, Green’s function methods, etc. 401

65N85

Fictitious domain methods 68

65N99

None of the above, but in this section 2532

65Pxx

Numerical problems in dynamical systems [See also 37Mxx] 2675

65P10

Hamiltonian systems including symplectic integrators 1281

65P20

Numerical chaos 469

65P30

Bifurcation problems 476

65P40

Nonlinear stabilities 291

65P99

None of the above, but in this section 240

65Qxx

Difference and functional equations, recurrence relations 1448

65Q10

Difference equations 217

65Q20

Functional equations 54

65Q30

Recurrence relations 137

65Q99

None of the above, but in this section 6

65Rxx

Integral equations, integral transforms 15058

65R10

Integral transforms 2082

65R20

Integral equations 12419

65R30

Improperly posed problems 952

65R32

Inverse problems 573

65R99

None of the above, but in this section 94

65Sxx

Graphical methods 494

65S05

Graphical methods 494

65S99

None of the above, but in this section 0

65Txx

Numerical methods in Fourier analysis 9101

65T40

Trigonometric approximation and interpolation 1829

65T50

Discrete and fast Fourier transforms 2736

65T60

Wavelets 4542

65T99

None of the above, but in this section 230

65Yxx

Computer aspects of numerical algorithms 15564

65Y04

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

65Y05

Parallel computation 9195

65Y10

Algorithms for specific classes of architectures 1065

65Y15

Packaged methods 1509

65Y20

Complexity and performance of numerical algorithms [See also 68Q25] 3815

65Y99

None of the above, but in this section 518

65Zxx

Applications to physics 7707

65Z05

Applications to physics 7607

65Z99

None of the above, but in this section 99

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