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Topic · Applied Mathematics

Differential Equations and Boundary Problems

Differential Equations and Boundary Problems is a research topic within Applied Mathematics. Science Explorer counts 26k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the study of nonlocal partial differential equations and boundary value problems, including topics such as solvability, numerical solutions, inverse problems, and the behavior of hyperbolic and parabolic equations with nonlocal conditions. The research also delves into the analysis of integro-differential equations and the properties of Green functions.

  • Nonlocal
  • Partial Differential Equations
  • Boundary Value Problems
  • Inverse Problem
  • Solvability
  • Numerical Solution
  • Hyperbolic Equations
  • Parabolic Equations
  • Integro-Differential Equations
  • Green Function
Research works
26k
fractional, since 1950
In the world top 10%
2.6k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+12%
the tick is no change
Largest producer
Russia
30% of the 10 largest, 2022-now
Differential Equations and Boundary Problems

Which countries lead Differential Equations and Boundary Problems research?

By volume, Russia and China publish the most (808 and 523 works in 2022-now).

By volume, 2022-now

  1. 1 Russia 808 works
  2. 2 China 523 works
  3. 3 India 249 works
  4. 4 Uzbekistan 200 works
  5. 5 United States 192 works
  6. 6 Ukraine 174 works
  7. 7 Kazakhstan 144 works
  8. 8 Türkiye 143 works
  9. 9 Saudi Arabia 117 works
  10. 10 Italy 110 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.

Russia: 30.4%China: 19.7%India: 9.4%Uzbekistan: 7.5%6 others listed: 33.1%30%largest
Russia808 · 30.4%China523 · 19.7%India249 · 9.4%Uzbekistan200 · 7.5%6 others listed880 · 33.1%

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

Which institutions lead Differential Equations and Boundary Problems research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Differential Equations and Boundary Problems research, followed by Lomonosov Moscow State University and National Academy of Sciences of Ukraine.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 191 works
  2. 2 Lomonosov Moscow State UniversityRussia 82 works
  3. 3 National Academy of Sciences of UkraineUkraine 53 works
  4. 4 Institute of Mathematics and Mathematical ModelingKazakhstan 46 works
  5. 5 Academy of Sciences Republic of UzbekistanUzbekistan 41 works
  6. 6 National University of UzbekistanUzbekistan 33 works
  7. 7 Peoples' Friendship University of RussiaRussia 32 works
  8. 8 Centre National de la Recherche ScientifiqueFrance 27 works
  9. 9 Université Sultan Moulay SlimaneMorocco 27 works
  10. 10 St Petersburg UniversityRussia 26 works

Who are the leading researchers in Differential Equations and Boundary Problems?

The most-cited researchers publishing on Differential Equations and Boundary Problems include Tasawar Hayat, Stanley Osher and John A. Todd.

  1. 1 Tasawar Hayat Pakistan 135k citations
  2. 2 Stanley Osher United States 119k citations
  3. 3 John A. Todd United Kingdom 107k citations
  4. 4 Simon A. Levin United States 106k citations
  5. 5 Jinde Cao China 104k citations

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

What are the most cited papers in Differential Equations and Boundary Problems?

The most cited paper in Differential Equations and Boundary Problems is "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators" (Cornelius Lanczos, 1950), with 4,448 citations. Next come "Compact sets in the spaceL p (O,T; B)" (4,138) and "Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I" (3,784).

Most cited papers
#PaperReleasedCitations
1 An iteration method for the solution of the eigenvalue problem of linear differential and integral operators Cornelius Lanczos · Journal of research of the National Bureau of Standards Oct 1950 4,448
2 Compact sets in the spaceL p (O,T; B) Jacques Simon · Annali di Matematica Pura ed Applicata (1923 -) Open access Dec 1986 4,138
3 Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I Shmuel Agmon, Avron Douglis, Louis Nirenberg · Communications on Pure and Applied Mathematics Nov 1959 3,784
4 Difference Methods for Initial-Value Problems Robert D. Richtmyer, E. H. Dill · Physics Today Open access Apr 1959 3,233
5 Ordinary differential equations, transport theory and Sobolev spaces Ronald J. DiPerna, Pierre Louis Lions · Inventiones mathematicae Oct 1989 2,007
All 99 most cited papers, with filters and sorting

Where is Differential Equations and Boundary Problems research done?

The largest centres of Differential Equations and Boundary Problems research in 2022-now are Moscow (Russia), Tashkent (Uzbekistan), Baku (Azerbaijan) and Almaty (Kazakhstan). Among places with at least 20 works in it, it is an unusually large share of all research in Beni Mellal, Chelyabinsk and Belgorod.

Largest cities, 2022-now

  1. 1 MoscowRussia 294 works
  2. 2 TashkentUzbekistan 117 works
  3. 3 BakuAzerbaijan 83 works
  4. 4 AlmatyKazakhstan 81 works
  5. 5 KyivUkraine 63 works
  6. 6 BeijingChina 58 works
  7. 7 NovosibirskRussia 43 works
  8. 8 ChelyabinskRussia 39 works
  9. 9 Saint PetersburgRussia 38 works
  10. 10 RiyadhSaudi Arabia 34 works

Where it is the local speciality

  1. Beni MellalMA · 27.3 works47×
  2. ChelyabinskRU · 39.1 works41×
  3. BelgorodRU · 24.4 works40×
← less than its size predicts1×more →

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

See Differential Equations and Boundary Problems on the map

Where is the best place to study Differential Equations and Boundary Problems?

Among universities, judged by research, Université Sultan Moulay Slimane, Qassim University and Vellore Institute of Technology 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%20%40%mean 20.54%fractional works in this field (log) →share of work in the world top 10% →Beijing Normal Unive…Vellore Institute of…Qassim UniversityUniversité Sultan Mo…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Université Sultan Moulay SlimaneMorocco 71.523.6%54.6×27 +364.2%
2Qassim UniversitySaudi Arabia 64.225.4%13.0×12 +58.3%
3Vellore Institute of Technology UniversityIndia 63.134.8%3.8×14 +73.6%
4Beijing Normal UniversityChina 59.737.7%3.6×10 +51.3%
5National University of UzbekistanUzbekistan 57.211.4%59.9×33 +14.7%
6Bukhara State UniversityUzbekistan 56.913.4%86.7×22 +411.3%
7Lomonosov Moscow State UniversityRussia 54.67.5%26.5×82 -11.9%
8Tashkent State University of EconomicsUzbekistan 51.523.9%22.4×10 -
9King Abdulaziz UniversitySaudi Arabia 50.319.8%6.4×13 -22.1%
10Peoples' Friendship University of RussiaRussia 46.27.9%27.7×32 -0.3%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Differential Equations and Boundary Problems, country by country

Is Differential Equations and Boundary Problems research growing?

Output in 2022-2025 was 12% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are Differential Equations and Boundary Problems.

still counting19801990200020102020
grewheldshrank

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

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Differential Equations and Boundary Problems as a percentage of every work published that year, 0.020% in 2024.

still counting0.020%0.040%0.060%Differential Equations and Boundary Problems0.017% in 202519801990200020102020

Fractional works of Differential Equations and Boundary Problems over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Differential Equations and Boundary Problems10.0% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

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