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Subfield · Mathematics

Numerical Analysis research

Numerical Analysis is a subfield of Mathematics. Science Explorer counts 130k research works in it since 1950. 14.2% of them reached the world's top 10% most cited for their field and year.

In short: study of algorithms that use numerical approximation for the problems of mathematical analysis.

Research works
130k
fractional, since 1950
In the world top 10%
19k
per year above
Top-10% rate
14.2%
share of its works in the world top 10%
Topics
5
Growth, 2013–17 → 2018–22
+12%
the tick is no change

What is Numerical Analysis research about, and what is growing?

By the world's output in 2019–23, its most used keywords are Numerical Methods, Singular Perturbation, Numerical Integration, Differential Equations, Exponential Integrators, Optimization Software. Gaining share since 2009–13: Iterative Methods, Newton's Method. Losing share: Optimization Software, Semidefinite Programming.

▲ gaining share of this field◆ holding its share▼ losing share

Size is the world's fractional works in 2019–23 in the topics tagged with each word; colour compares the word's share of this field with 2009–13. Each links to the topic it comes from most.

All 11 words, with their numbers
  1. Numerical Methods7,288◆ 1.12×1 topic
  2. Singular Perturbation7,288◆ 1.12×1 topic
  3. Numerical Integration7,164◆ 0.95×2 topics
  4. Differential Equations5,545◆ 0.93×1 topic
  5. Exponential Integrators5,545◆ 0.93×1 topic
  6. Optimization Software4,676▼ 0.84×1 topic
  7. Semidefinite Programming4,676▼ 0.84×1 topic
  8. Iterative Methods3,460▲ 1.16×1 topic
  9. Newton's Method3,460▲ 1.16×1 topic
  10. High-dimensional Integration1,618◆ 1.02×1 topic
  11. Quasi-Monte Carlo1,618◆ 1.02×1 topic

Which countries lead Numerical Analysis research?

On research quality in 2022–2025, China, India and the United States rank highest in Numerical Analysis. By volume, China and the United States publish the most (3.6k and 1.6k works in 2022–2025).

By research quality, 2022–2025

  1. 1 China · #2 all time 12.7% top 10% · 3.6k works
  2. 2 India · #8 all time 12.8% top 10% · 1.6k works
  3. 3 United States · #1 all time 11.8% top 10% · 1.6k works
  4. 4 Saudi Arabia · #9 all time 20.9% top 10% · 529 works
  5. 5 Türkiye · #14 all time 13.7% top 10% · 554 works
  6. 6 Egypt · #16 all time 23.5% top 10% · 242 works
  7. 7 Italy · #7 all time 16.2% top 10% · 427 works
  8. 8 Germany · #3 all time 11.8% top 10% · 598 works
  9. 9 Iran · #10 all time 12.0% top 10% · 502 works
  10. 10 Russia · #11 all time 5.4% top 10% · 1.2k works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 20 countries ranked in Numerical Analysis. Composite of field-normalised excellence (50%), output (30%) and citations (20%); the bracket is the all-time rank.

All countries ranked in Numerical Analysis

By volume, 2022–2025

  1. 1 China 3.6k works
  2. 2 United States 1.6k works
  3. 3 India 1.6k works
  4. 4 Russia 1.2k works
  5. 5 Germany 598 works
  6. 6 Türkiye 554 works
  7. 7 Saudi Arabia 529 works
  8. 8 Iran 502 works
  9. 9 France 476 works
  10. 10 Italy 427 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 32.4%United States: 14.2%India: 14.2%Russia: 11.2%6 others listed: 27.9%32%largest
China3,585 · 32.4%United States1,575 · 14.2%India1,575 · 14.2%Russia1,237 · 11.2%6 others listed3,086 · 27.9%

Shares of the rows listed above, not of the whole node.

Which institutions lead Numerical Analysis research?

Lomonosov Moscow State University (Russia) ranks first in Numerical Analysis on research quality in 2022–2025, followed by Centre National de la Recherche Scientifique and Russian Academy of Sciences.

By research quality, 2022–2025

  1. 1 Lomonosov Moscow State University Russia · Moscow · #37 all time 9.5% top 10% · 115 works
  2. 2 Centre National de la Recherche Scientifique France · Paris · #13 all time 9.3% top 10% · 64 works
  3. 3 Russian Academy of Sciences Russia · Moscow · #94 all time 5.8% top 10% · 60 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 3 institutions above the floor of 40 fractional works in Numerical Analysis.

Top 100 Numerical Analysis institutions

By volume, 2022–2025

  1. 1 Lomonosov Moscow State University Russia 115 works
  2. 2 Centre National de la Recherche Scientifique France 64 works
  3. 3 Russian Academy of Sciences Russia 60 works
  4. 4 University of Mosul Iraq 54 works
  5. 5 King Abdulaziz University Saudi Arabia 51 works
  6. 6 Harbin Institute of Technology China 51 works
  7. 7 Qassim University Saudi Arabia 51 works
  8. 8 St Petersburg University Russia 48 works
  9. 9 Shandong University China 47 works
  10. 10 Vellore Institute of Technology University India 47 works

Who are the leading researchers in Numerical Analysis?

Among the most productive authors in Numerical Analysis, Stanley Osher, George Em Karniadakis and Kalyanmoy Deb rank highest on the composite score.

  1. 1 Stanley Osher United States · #48 worldwide 8k citations · 207 works
  2. 2 George Em Karniadakis United States · #151 worldwide 6.3k citations · 268 works
  3. 3 Kalyanmoy Deb United States · #287 worldwide 6.7k citations · 218 works
  4. 4 N. J. A. Sloane United States · #887 worldwide 2.8k citations · 116 works
  5. 5 Ivo Babuška United States · #975 worldwide 2.7k citations · 110 works
  6. 6 A. Charnes United States · #1,082 worldwide 4.5k citations · 88 works
  7. 7 John C. Doyle United States · #1,162 worldwide 3.3k citations · 93 works
  8. 8 Dimitri P. Bertsekas United States · #1,409 worldwide 1.8k citations · 103 works
  9. 9 Peter D. Lax United States · #1,685 worldwide 2k citations · 82 works
  10. 10 P.V. Kokotović United States · #1,691 worldwide 2.6k citations · 115 works

Re-ranked on the composite score from the 4,373 highest-output authors in Numerical Analysis. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Numerical Analysis researchers

Where is Numerical Analysis research done?

The largest centres of Numerical Analysis research in 2022–2025 are Moscow (Russia), Beijing (China), Shanghai (China) and Nanjing (China). Among places with at least 20 works in it, it is an unusually large share of all research in Lawton.

Largest cities, 2022–2025

  1. 1 Moscow Russia 508 works
  2. 2 Beijing China 403 works
  3. 3 Shanghai China 250 works
  4. 4 Nanjing China 177 works
  5. 5 Riyadh Saudi Arabia 143 works
  6. 6 Xi'an China 142 works
  7. 7 Changsha China 141 works
  8. 8 Paris France 140 works
  9. 9 Guangzhou China 138 works
  10. 10 Tehran Iran 132 works

Where it is the local speciality

  1. LawtonUS · 38.7 works284×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Numerical Analysis than the world average.

See Numerical Analysis on the map

Numerical Analysis research by country

The best places for Numerical Analysis research inside each country, with that country's researchers and world standing.

Where is the best place to study Numerical Analysis?

Among universities, judged by research, China Medical University, Prince Sultan University and Qassim University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%25%50%75%mean 33.62%fractional works in this node (log) →share in the world top 10% →China Medical University: 39, 32.6%Prince Sultan University: 27, 30.9%Qassim University: 51, 20.7%Hunan University of Technology: 25, 67.4%National Institute of Technology Rourkela: 40, 21.8%Al-Balqa Applied University: 20, 43.5%Zarqa University: 18, 20.3%Lesya Ukrainka Volyn National University: 12, 42.0%University of Malakand: 12, 27.4%Lebanese American University: 23, 29.6%Hunan University of …China Medical Univer…Prince Sultan Univer…Qassim University
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1China Medical University Taiwan 70.132.6%16.1×39 +1546.9%
2Prince Sultan University Saudi Arabia 68.230.9%13.8×27 +213.2%
3Qassim University Saudi Arabia 66.720.7%11.2×51 +192.0%
4Hunan University of Technology China 64.367.4%13.2×25 -20.6%
5National Institute of Technology Rourkela India 61.121.8%9.9×40 +395.9%
6Al-Balqa Applied University Jordan 60.343.5%10.8×20 +77.2%
7Zarqa University Jordan 59.520.3%12.7×18 +281.2%
8Lesya Ukrainka Volyn National University Ukraine 58.942.0%9.7×12 +363.5%
9University of Malakand Pakistan 58.227.4%14.0×12 +345.7%
10Lebanese American University Lebanon 57.929.6%11.6×23 —

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Numerical Analysis research growing?

Output in 2018–2022 was 12% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are Iterative Methods for Nonlinear Equations, Differential Equations and Numerical Methods and Mathematical Approximation and Integration.

19801990200020102020
grewheldshrank

The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

  1. Iterative Methods for Nonlinear Equations+45%
  2. Differential Equations and Numerical Methods+28%
  3. Mathematical Approximation and Integration+26%
  4. Numerical methods for differential equations+14%
  5. Advanced Optimization Algorithms Research+14%
← shrinkingno changegrowing →

Growth in output from 2005–09 to 2015–19. Every topic is a page of its own.

What does Numerical Analysis include?

Numerical methods for di…37kNumerical methods for differential equations: 37k fractional worksDifferential Equations a…36kDifferential Equations and Numerical Methods: 36k fractional worksAdvanced Optimization Al…30kAdvanced Optimization Algorithms Research: 30k fractional worksIterative Methods for No…17kIterative Methods for Nonlinear Equations: 17k fractional worksMathematical Approximati…10kMathematical Approximation and Integration: 10k fractional works

Area is fractional works in that topic. Every name below is a page of its own.