Numerical methods for differential equations
Numerical methods for differential equations is a research topic within Numerical Analysis. Science Explorer counts 37k research works in it since 1950. 14.9% of them reached the world's top 10% most cited for their field and year.
This cluster of papers focuses on the development and analysis of numerical integration methods for solving differential equations, with a particular emphasis on exponential integrators, symplectic methods, time-stepping schemes, and variational integrators. The research covers a wide range of applications including the numerical solution of the Schrödinger equation, Hamiltonian systems, and matrix exponential computations.
- Numerical Integration
- Differential Equations
- Exponential Integrators
- Symplectic Methods
- Time-Stepping Schemes
- Variational Integrators
- Matrix Exponential
- Runge-Kutta Methods
- Schrödinger Equation
- Hamiltonian Systems
- Research works
- 37k fractional, since 1950
- In the world top 10%
- 5.6k per year above
- Top-10% rate
- 14.9% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- +5% the tick is no change
Which countries lead Numerical methods for differential equations research?
By volume, China and the United States publish the most (1k and 497 works in 2022–2025).
By volume, 2022–2025
- 1 China 1k works
- 2 United States 497 works
- 3 India 306 works
- 4 Germany 254 works
- 5 Russia 211 works
- 6 France 180 works
- 7 Italy 145 works
- 8 Saudi Arabia 121 works
- 9 Nigeria 115 works
- 10 Iran 115 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 Numerical methods for differential equations research?
By volume in 2022–2025, Centre National de la Recherche Scientifique publishes the most Numerical methods for differential equations research, followed by Technical University of Munich and Xi'an Jiaotong University.
By volume, 2022–2025
- 1 Centre National de la Recherche Scientifique France 27 works
- 2 Technical University of Munich Germany 26 works
- 3 Xi'an Jiaotong University China 23 works
- 4 Harbin Institute of Technology China 23 works
- 5 Huazhong University of Science and Technology China 18 works
- 6 Shandong University China 18 works
- 7 Xiangtan University China 16 works
- 8 Shanghai University China 15 works
- 9 National University of Defense Technology China 15 works
- 10 Zhengzhou University China 14 works
Who are the leading researchers in Numerical methods for differential equations?
The most-cited researchers publishing on Numerical methods for differential equations include Stanley Osher, George Em Karniadakis and Xuemin Shen.
- 1 Stanley Osher 8k citations
- 2 George Em Karniadakis 6.3k citations
- 3 Xuemin Shen 5.1k citations
- 4 Jinde Cao 4.2k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Numerical methods for differential equations research done?
The largest centres of Numerical methods for differential equations research in 2022–2025 are Beijing (China), Moscow (Russia), Shanghai (China) and Nanjing (China). Among places with at least 20 works in it, it is an unusually large share of all research in Xiangtan.
Largest cities, 2022–2025
Where it is the local speciality
- XiangtanCN · 20.7 works9.8×
Location quotient: how much more of its research is in Numerical methods for differential equations than the world average.
Where is the best place to study Numerical methods for differential equations?
Among universities, judged by research, Hunan University of Technology, Qassim University and Van Yüzüncü Yıl Üniversitesi 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 | 61.7 | 61.7% | 18.7× | 9 | +19.0% |
| 2 | Qassim University Saudi Arabia | 54.4 | 18.7% | 11.0× | 13 | — |
| 3 | Van Yüzüncü Yıl Üniversitesi Türkiye | 51.2 | 33.1% | 10.6× | 11 | +46.7% |
| 4 | Technical University of Munich Germany | 46.5 | 4.3% | 7.3× | 26 | +4.0% |
| 5 | University of Tabriz Iran | 45.0 | 3.6% | 12.1× | 13 | +73.7% |
| 6 | University of Wuppertal Germany | 44.6 | 16.6% | 17.7× | 12 | +24.1% |
| 7 | Xiangtan University China | 43.2 | 7.8% | 14.8× | 16 | -6.7% |
| 8 | Georgia Southern University United States | 43.2 | 4.0% | 18.8× | 8 | +319.1% |
| 9 | University of Freiburg Germany | 42.1 | 19.3% | 5.8× | 9 | +177.8% |
| 10 | Karlsruhe Institute of Technology Germany | 41.1 | 15.3% | 4.6× | 11 | +236.4% |
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 methods for differential equations research growing?
Output in 2018–2022 was 5% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Numerical methods for differential equations.
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.