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Mathematics Subject Classification – MSC2020

65-XX

Numerical analysis 298626

65-00

General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to numerical analysis 137

65-01

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis 2181

65-02

Research exposition (monographs, survey articles) pertaining to numerical analysis 2502

65-03

History of numerical analysis [Consider also classification numbers pertaining to Section 01-XX] 498

65-04

Software, source code, etc. for problems pertaining to numerical analysis 859

65-06

Proceedings, conferences, collections, etc. pertaining to numerical analysis 3655

65-11

Research data for problems pertaining to numerical analysis 0

65Axx

Tables in numerical analysis 519

65A05

Tables in numerical analysis 503

65A99

None of the above, but in this section 11

65Bxx

Acceleration of convergence in numerical analysis 2103

65B05

Extrapolation to the limit, deferred corrections 943

65B10

Numerical summation of series 683

65B15

Euler-Maclaurin formula in numerical analysis 311

65B99

None of the above, but in this section 267

65Cxx

Probabilistic methods, stochastic differential equations 41354

65C05

Monte Carlo methods [See also 82M31] 12842

65C10

Random number generation in numerical analysis [See also 11K45] 2537

65C20

Probabilistic models, generic numerical methods in probability and statistics [See also 60-08, 62-08] 4413

65C30

Numerical solutions to stochastic differential and integral equations {For theoretical aspects, see 60H35} [See also 65M75, 65N75] 3363

65C35

Stochastic particle methods [See also 82M60] 382

65C40

Numerical analysis or methods applied to Markov chains [See also 60J22] 2488

65C99

None of the above, but in this section 5057

65Dxx

Numerical approximation and computational geometry (primarily algorithms) {For theoretical aspects, see 41-XX, 68Uxx} 34435

65D05

Numerical interpolation 5522

65D07

Numerical computation using splines 5461

65D10

Numerical smoothing, curve fitting 3110

65D12

Numerical radial basis function approximation 8

65D15

Algorithms for approximation of functions 2664

65D17

Computer-aided design (modeling of curves and surfaces) [See also 68U07] 5039

65D18

Numerical aspects of computer graphics, image analysis, and computational geometry [See also 51N05, 68U05] 4775

65D19

Computational issues in computer and robotic vision 65

65D20

Computation of special functions and constants, construction of tables [See also 33F05] 2582

65D25

Numerical differentiation 1532

65D30

Numerical integration 3614

65D32

Numerical quadrature and cubature formulas 5432

65D40

High-dimensional functions; sparse grids 1

65D99

None of the above, but in this section 542

65Exx

Numerical methods in complex analysis (potential theory, etc.) 1422

65E05

General theory of numerical methods in complex analysis (potential theory, etc.) [See also 30-08, 31-08, 32-08] 1415

65E10

Numerical methods in conformal mappings [See also 30C30] 2

65E99

None of the above, but in this section 6

65Fxx

Numerical linear algebra 38490

65F05

Direct numerical methods for linear systems and matrix inversion 5856

65F08

Preconditioners for iterative methods 2184

65F10

Iterative numerical methods for linear systems [See also 65N22] 14244

65F15

Numerical computation of eigenvalues and eigenvectors of matrices 7184

65F18

Numerical solutions to inverse eigenvalue problems 441

65F20

Numerical solutions to overdetermined systems, pseudoinverses 3617

65F22

Ill-posedness and regularization problems in numerical linear algebra 1099

65F25

Orthogonalization in numerical linear algebra 759

65F35

Numerical computation of matrix norms, conditioning, scaling [See also 15A12, 15A60] 4758

65F40

Numerical computation of determinants 465

65F45

Numerical methods for matrix equations 41

65F50

Computational methods for sparse matrices 3869

65F55

Numerical methods for low-rank matrix approximation; matrix compression 38

65F60

Numerical computation of matrix exponential and similar matrix functions 323

65F99

None of the above, but in this section 630

65Gxx

Error analysis and interval analysis 5907

65G20

Algorithms with automatic result verification 451

65G30

Interval and finite arithmetic 2771

65G40

General methods in interval analysis 607

65G50

Roundoff error 1886

65G99

None of the above, but in this section 414

65Hxx

Nonlinear algebraic or transcendental equations 12526

65H04

Numerical computation of roots of polynomial equations 541

65H05

Numerical computation of solutions to single equations 4268

65H10

Numerical computation of solutions to systems of equations 6634

65H14

Numerical algebraic geometry 5

65H17

Numerical solution of nonlinear eigenvalue and eigenvector problems [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30] 584

65H20

Global methods, including homotopy approaches to the numerical solution of nonlinear equations [See also 58C30, 90C30] 755

65H99

None of the above, but in this section 124

65Jxx

Numerical analysis in abstract spaces 11839

65J05

General theory of numerical analysis in abstract spaces 1674

65J08

Numerical solutions to abstract evolution equations 192

65J10

Numerical solutions to equations with linear operators (do not use 65Fxx) 2845

65J15

Numerical solutions to equations with nonlinear operators (do not use 65Hxx) 5015

65J20

Numerical solutions of ill-posed problems in abstract spaces; regularization 1743

65J22

Numerical solution to inverse problems in abstract spaces 725

65J99

None of the above, but in this section 1122

65Kxx

Numerical methods for mathematical programming, optimization and variational techniques 31047

65K05

Numerical mathematical programming methods [See also 90Cxx] 19948

65K10

Numerical optimization and variational techniques [See also 49Mxx, 93-08] 10273

65K15

Numerical methods for variational inequalities and related problems 1045

65K99

None of the above, but in this section 181

65Lxx

Numerical methods for ordinary differential equations 29512

65L03

Numerical methods for functional-differential equations 496

65L04

Numerical methods for stiff equations 475

65L05

Numerical methods for initial value problems 12197

65L06

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 5910

65L07

Numerical investigation of stability of solutions 752

65L08

Numerical solution of ill-posed problems involving ordinary differential equations 69

65L09

Numerical solution of inverse problems involving ordinary differential equations 333

65L10

Numerical solution of boundary value problems involving ordinary differential equations 7325

65L11

Numerical solution of singularly perturbed problems involving ordinary differential equations 410

65L12

Finite difference and finite volume methods for ordinary differential equations 2454

65L15

Numerical solution of eigenvalue problems involving ordinary differential equations 1696

65L20

Stability and convergence of numerical methods for ordinary differential equations 5565

65L50

Mesh generation, refinement, and adaptive methods for ordinary differential equations 1410

65L60

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 3136

65L70

Error bounds for numerical methods for ordinary differential equations 2210

65L80

Numerical methods for differential-algebraic equations 892

65L99

None of the above, but in this section 1611

65Mxx

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 45968

65M06

Finite difference methods for initial value and initial-boundary value problems involving PDEs 15866

65M08

Finite volume methods for initial value and initial-boundary value problems involving PDEs 2480

65M12

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 13134

65M15

Error bounds for initial value and initial-boundary value problems involving PDEs 6330

65M20

Method of lines for initial value and initial-boundary value problems involving PDEs 3065

65M22

Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs [See also 65Fxx, 65Hxx] 503

65M25

Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs 1155

65M30

Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs 888

65M32

Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs 1743

65M38

Boundary element methods for initial value and initial-boundary value problems involving PDEs 339

65M50

Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 2690

65M55

Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs 2119

65M60

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 11318

65M70

Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 5204

65M75

Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs 866

65M80

Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value problems involving PDEs 199

65M85

Fictitious domain methods for initial value and initial-boundary value problems involving PDEs 89

65M99

None of the above, but in this section 2922

65Nxx

Numerical methods for partial differential equations, boundary value problems 52070

65N06

Finite difference methods for boundary value problems involving PDEs 6692

65N08

Finite volume methods for boundary value problems involving PDEs 669

65N12

Stability and convergence of numerical methods for boundary value problems involving PDEs 9057

65N15

Error bounds for boundary value problems involving PDEs 8531

65N20

Numerical methods for ill-posed problems for boundary value problems involving PDEs 309

65N21

Numerical methods for inverse problems for boundary value problems involving PDEs 1552

65N22

Numerical solution of discretized equations for boundary value problems involving PDEs [See also 65Fxx, 65Hxx] 3881

65N25

Numerical methods for eigenvalue problems for boundary value problems involving PDEs 2300

65N30

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 24033

65N35

Spectral, collocation and related methods for boundary value problems involving PDEs 4051

65N38

Boundary element methods for boundary value problems involving PDEs 4179

65N40

Method of lines for boundary value problems involving PDEs 485

65N45

Method of contraction of the boundary for boundary value problems involving PDEs 37

65N50

Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 4559

65N55

Multigrid methods; domain decomposition for boundary value problems involving PDEs 5392

65N75

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs 249

65N80

Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs 533

65N85

Fictitious domain methods for boundary value problems involving PDEs 103

65N99

None of the above, but in this section 2603

65Pxx

Numerical problems in dynamical systems [See also 37Mxx] 2958

65P10

Numerical methods for Hamiltonian systems including symplectic integrators 1445

65P20

Numerical chaos 506

65P30

Numerical bifurcation problems 510

65P40

Numerical nonlinear stabilities in dynamical systems 330

65P99

None of the above, but in this section 262

65Qxx

Numerical methods for difference and functional equations, recurrence relations 1518

65Q10

Numerical methods for difference equations 254

65Q20

Numerical methods for functional equations 62

65Q30

Numerical aspects of recurrence relations 173

65Q99

None of the above, but in this section 7

65Rxx

Numerical methods for integral equations, integral transforms 15974

65R10

Numerical methods for integral transforms 2180

65R15

Numerical methods for eigenvalue problems in integral equations 3

65R20

Numerical methods for integral equations 13134

65R30

Numerical methods for ill-posed problems for integral equations 980

65R32

Numerical methods for inverse problems for integral equations 651

65R99

None of the above, but in this section 98

65Sxx

Graphical methods in numerical analysis 518

65S05

Graphical methods in numerical analysis 517

65S99

None of the above, but in this section 0

65Txx

Numerical methods in Fourier analysis 9734

65T40

Numerical methods for trigonometric approximation and interpolation 1872

65T50

Numerical methods for discrete and fast Fourier transforms 2985

65T60

Numerical methods for wavelets 4863

65T99

None of the above, but in this section 252

65Yxx

Computer aspects of numerical algorithms 16172

65Y04

Numerical algorithms for computer arithmetic, etc. [See also 68M07] 463

65Y05

Parallel numerical computation 9623

65Y10

Numerical algorithms for specific classes of architectures 1169

65Y15

Packaged methods for numerical algorithms 1566

65Y20

Complexity and performance of numerical algorithms [See also 68Q25] 3994

65Y99

None of the above, but in this section 529

65Zxx

Applications to the sciences 7838

65Z05

Applications to the sciences 7734

65Z99

None of the above, but in this section 98

Overview

General and overarching topics; collections

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

Approximations 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, finance, and other social and behavioral sciences

Biology and other natural sciences

Systems theory; control

Information and communication theory, circuits

Mathematics education

any	anywhere
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

zbMATH — the first resource for mathematics

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Mathematics Subject Classification – MSC2020

Overview