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 China 1.2k works
- 2 Russia 703 works
- 3 India 530 works
- 4 United States 257 works
- 5 Saudi Arabia 221 works
- 6 Türkiye 180 works
- 7 Iran 158 works
- 8 Uzbekistan 140 works
- 9 Ukraine 116 works
- 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.
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 Lomonosov Moscow State University Russia 72 works
- 2 Russian Academy of Sciences Russia 31 works
- 3 Institute of Mathematics and Mathematical Modeling Kazakhstan 26 works
- 4 National Institute of Technology Rourkela India 25 works
- 5 Academy of Sciences Republic of Uzbekistan Uzbekistan 25 works
- 6 National University of Uzbekistan Uzbekistan 25 works
- 7 Qassim University Saudi Arabia 24 works
- 8 Peoples' Friendship University of Russia Russia 24 works
- 9 Shandong University China 24 works
- 10 Jimma University Ethiopia 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 Stanley Osher 8k citations
- 2 George Em Karniadakis 6.3k citations
- 3 Jinde Cao 4.2k citations
- 4 Louis Nirenberg 2.9k citations
- 5 P.V. Kokotović 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
Where it is the local speciality
- JimmaET · 22.9 works33×
Location quotient: how much more of its research is in Differential Equations and Numerical Methods than the world average.
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.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Hunan University of Technology China | 63.0 | 74.6% | 25.2× | 15 | -21.5% |
| 2 | Qassim University Saudi Arabia | 62.8 | 19.5% | 17.0× | 24 | +357.4% |
| 3 | Lomonosov Moscow State University Russia | 61.8 | 10.7% | 15.3× | 72 | +98.1% |
| 4 | National Institute of Technology Rourkela India | 60.4 | 23.3% | 19.8× | 25 | +949.1% |
| 5 | Imam Mohammad ibn Saud Islamic University Saudi Arabia | 57.4 | 35.5% | 13.3× | 14 | +68.1% |
| 6 | Prince Sattam Bin Abdulaziz University Saudi Arabia | 56.9 | 36.0% | 9.4× | 14 | +77.1% |
| 7 | National University of Uzbekistan Uzbekistan | 55.1 | 7.1% | 29.7× | 25 | +219.4% |
| 8 | Prince Sultan University Saudi Arabia | 54.4 | 31.7% | 19.8× | 12 | — |
| 9 | Jimma University Ethiopia | 53.6 | 27.1% | 33.9× | 23 | — |
| 10 | Lebanese American University Lebanon | 50.9 | 27.9% | 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.
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.