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Topic · Numerical Analysis

Differential Equations and Numerical Methods

Differential Equations and Numerical Methods is a research topic within Numerical Analysis. Science Explorer counts 36k research works in it since 1950. 11.8% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on numerical methods and analysis for solving singularly perturbed problems, particularly in the context of convection-diffusion and reaction-diffusion equations. The research covers topics such as boundary layers, finite difference schemes, asymptotic analysis, parameter-robust methods, and adaptive meshes to accurately solve these challenging problems.

  • Singular Perturbation
  • Numerical Methods
  • Convection-Diffusion Problems
  • Boundary Layers
  • Finite Difference Schemes
  • Asymptotic Analysis
  • Parameter-Robust Methods
  • Reaction-Diffusion Equations
  • Adaptive Meshes
  • Error Analysis
Research works
36k
fractional, since 1950
In the world top 10%
4.3k
per year above
Top-10% rate
11.8%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+23%
the tick is no change

Which countries lead Differential Equations and Numerical Methods research?

By volume, China and Russia publish the most (1.2k and 703 works in 2022–2025).

By volume, 2022–2025

  1. 1 China 1.2k works
  2. 2 Russia 703 works
  3. 3 India 530 works
  4. 4 United States 257 works
  5. 5 Saudi Arabia 221 works
  6. 6 Türkiye 180 works
  7. 7 Iran 158 works
  8. 8 Uzbekistan 140 works
  9. 9 Ukraine 116 works
  10. 10 Egypt 114 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: 33.8%Russia: 19.2%India: 14.5%United States: 7.0%6 others listed: 25.4%34%largest
China1,233 · 33.8%Russia703 · 19.2%India530 · 14.5%United States257 · 7.0%6 others listed929 · 25.4%

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

Which institutions lead Differential Equations and Numerical Methods research?

By volume in 2022–2025, Lomonosov Moscow State University publishes the most Differential Equations and Numerical Methods research, followed by Russian Academy of Sciences and Institute of Mathematics and Mathematical Modeling.

By volume, 2022–2025

  1. 1 Lomonosov Moscow State UniversityRussia 72 works
  2. 2 Russian Academy of SciencesRussia 31 works
  3. 3 Institute of Mathematics and Mathematical ModelingKazakhstan 26 works
  4. 4 National Institute of Technology RourkelaIndia 25 works
  5. 5 Academy of Sciences Republic of UzbekistanUzbekistan 25 works
  6. 6 National University of UzbekistanUzbekistan 25 works
  7. 7 Qassim UniversitySaudi Arabia 24 works
  8. 8 Peoples' Friendship University of RussiaRussia 24 works
  9. 9 Shandong UniversityChina 24 works
  10. 10 Jimma UniversityEthiopia 23 works

Who are the leading researchers in Differential Equations and Numerical Methods?

The most-cited researchers publishing on Differential Equations and Numerical Methods include Stanley Osher, George Em Karniadakis and Jinde Cao.

  1. 1 Stanley Osher United States 8k citations
  2. 2 George Em Karniadakis United States 6.3k citations
  3. 3 Jinde Cao China 4.2k citations
  4. 4 Louis Nirenberg United States 2.9k citations
  5. 5 P.V. Kokotović United States 2.6k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

Where is Differential Equations and Numerical Methods research done?

The largest centres of Differential Equations and Numerical Methods research in 2022–2025 are Moscow (Russia), Beijing (China), Tashkent (Uzbekistan) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Jimma.

Largest cities, 2022–2025

  1. 1 Moscow Russia 272 works
  2. 2 Beijing China 114 works
  3. 3 Tashkent Uzbekistan 89 works
  4. 4 Shanghai China 82 works
  5. 5 Jinan China 68 works
  6. 6 Riyadh Saudi Arabia 62 works
  7. 7 Nanjing China 60 works
  8. 8 Almaty Kazakhstan 57 works
  9. 9 Guangzhou China 54 works
  10. 10 Kyiv Ukraine 51 works

Where it is the local speciality

  1. JimmaET · 22.9 works33×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Differential Equations and Numerical Methods than the world average.

See Differential Equations and Numerical Methods on the map

Where is the best place to study Differential Equations and Numerical Methods?

Among universities, judged by research, Hunan University of Technology, Qassim University and Lomonosov Moscow State 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%50%100%mean 29.34%fractional works in this node (log) →share in the world top 10% →Hunan University of Technology: 15, 74.6%Qassim University: 24, 19.5%Lomonosov Moscow State University: 72, 10.7%National Institute of Technology Rourkela: 25, 23.3%Imam Mohammad ibn Saud Islamic University: 14, 35.5%Prince Sattam Bin Abdulaziz University: 14, 36.0%National University of Uzbekistan: 25, 7.1%Prince Sultan University: 12, 31.7%Jimma University: 23, 27.1%Lebanese American University: 9, 27.9%Hunan University of …National Institute o…Qassim UniversityLomonosov Moscow Sta…
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
1 Hunan University of TechnologyChina 63.074.6%25.2×15 -21.5%
2 Qassim UniversitySaudi Arabia 62.819.5%17.0×24 +357.4%
3 Lomonosov Moscow State UniversityRussia 61.810.7%15.3×72 +98.1%
4 National Institute of Technology RourkelaIndia 60.423.3%19.8×25 +949.1%
5 Imam Mohammad ibn Saud Islamic UniversitySaudi Arabia 57.435.5%13.3×14 +68.1%
6 Prince Sattam Bin Abdulaziz UniversitySaudi Arabia 56.936.0%9.4×14 +77.1%
7 National University of UzbekistanUzbekistan 55.17.1%29.7×25 +219.4%
8 Prince Sultan UniversitySaudi Arabia 54.431.7%19.8×12 —
9 Jimma UniversityEthiopia 53.627.1%33.9×23 —
10 Lebanese American UniversityLebanon 50.927.9%14.8×9 —

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 Differential Equations and Numerical Methods research growing?

Output in 2018–2022 was 23% higher than in 2013–2017, peaking in 2024. The fastest-growing topics are Differential Equations and Numerical Methods.

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.