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Topic · Modeling and Simulation

Mathematical and Computational Methods

Mathematical and Computational Methods is a research topic within Modeling and Simulation. Science Explorer counts 1.1k research works in it since 1950. 9.9% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers a wide range of topics related to mathematical modeling, including interpolation, partial fractions, differential equations, numerical analysis, computational mathematics, algorithms, nonlinear dynamics, and mathematical education. The papers explore applications of mathematical modeling in various fields such as physics, engineering, economics, and law.

  • Mathematica
  • Interpolation
  • Partial Fractions
  • Differential Equations
  • Numerical Analysis
  • Modeling
  • Algorithm
  • Computational Mathematics
  • Nonlinear Dynamics
  • Mathematical Education
Research works
1.1k
fractional, since 1950
In the world top 10%
112
per year above
Top-10% rate
9.9%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+26%
the tick is no change
Largest producer
United States
45% of the 10 largest, 2022-now
Mathematical and Computational Methods

Which countries lead Mathematical and Computational Methods research?

By volume, the United States and the United Kingdom publish the most (65 and 14 works in 2022-now).

By volume, 2022-now

  1. 1 United States 65 works
  2. 2 United Kingdom 14 works
  3. 3 Tonga 11 works
  4. 4 Russia 10 works
  5. 5 Germany 9 works
  6. 6 India 9 works
  7. 7 China 7 works
  8. 8 Brazil 6 works
  9. 9 Türkiye 6 works
  10. 10 Mexico 6 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.

United States: 45.0%United Kingdom: 9.7%Tonga: 7.9%Russia: 7.1%6 others listed: 30.4%45%largest
United States65 · 45.0%United Kingdom14 · 9.7%Tonga11 · 7.9%Russia10 · 7.1%6 others listed44 · 30.4%

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

Which institutions lead Mathematical and Computational Methods research?

By volume in 2022-now, Atenisi Institute publishes the most Mathematical and Computational Methods research, followed by Occidental College and Ostim Technical University.

By volume, 2022-now

  1. 1 Atenisi InstituteTonga 11 works
  2. 2 Occidental CollegeUnited States 10 works
  3. 3 Ostim Technical UniversityTürkiye 4 works
  4. 4 American Society of GenealogistsUnited States 4 works
  5. 5 London School of Economics and Political ScienceUnited Kingdom 3 works
  6. 6 Moscow State University of Civil EngineeringRussia 2 works
  7. 7 Secretariat of Public EducationMexico 2 works
  8. 8 Claremont CollegesUnited States 2 works
  9. 9 University of MontanaUnited States 2 works
  10. 10 University of IbadanNigeria 2 works

Who are the leading researchers in Mathematical and Computational Methods?

The most-cited researchers publishing on Mathematical and Computational Methods include Richard Bellman.

  1. 1 Richard Bellman United States 80k 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 Mathematical and Computational Methods?

The most cited paper in Mathematical and Computational Methods is "Theory of Linear and Integer Programming" (Adam N. Letchford, Alexander Schrijver, 2000), with 5,691 citations. Next come "Generating Feynman diagrams and amplitudes with FeynArts 3" (1,939) and "A QUANTITATIVE ANALYSIS OF PLANT FORM-THE PIPE MODEL THEORY : I.BASIC ANALYSES" (1,146).

Most cited papers
#PaperReleasedCitations
1 Theory of Linear and Integer Programming Adam N. Letchford, Alexander Schrijver · Journal of the Operational Research Society Jul 2000 5,691
2 Generating Feynman diagrams and amplitudes with FeynArts 3 Thomas Hahn · Computer Physics Communications Open access Nov 2001 1,939
3 A QUANTITATIVE ANALYSIS OF PLANT FORM-THE PIPE MODEL THEORY : I.BASIC ANALYSES Kichiro Shinozaki, Kyoji Yoda, Kazuo Hozumi et al. · Nihon Seitai Gakkaishi Open access Jun 1964 1,146
4 Mathematical and computer modelling ErvinY. Rodin · Mathematical and Computer Modelling Open access 1989 685
5 CRITIQUE OF DIALECTICAL REASON Wolfe Mays · Philosophical Books 1978 488
All 100 most cited papers, with filters and sorting

Where is Mathematical and Computational Methods research done?

The largest centres of Mathematical and Computational Methods research in 2022-now are Nuku'alofa (Tonga), Los Angeles (United States), Moscow (Russia) and London (United Kingdom).

Largest cities, 2022-now

  1. 1 Nuku'alofaTonga 11 works
  2. 2 Los AngelesUnited States 11 works
  3. 3 MoscowRussia 6 works
  4. 4 LondonUnited Kingdom 6 works
  5. 5 AnkaraTürkiye 4 works
  6. 6 SharonUnited States 4 works
  7. 7 BeijingChina 3 works
  8. 8 Mexico CityMexico 3 works
  9. 9 BakuAzerbaijan 3 works
  10. 10 RomeItaly 2 works
See Mathematical and Computational Methods on the map

Where is the best place to study Mathematical and Computational Methods?

Among universities, judged by research, Occidental College and Atenisi Institute 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.

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
1Occidental CollegeUnited States 45.09.1%3143.6×10 -
2Atenisi InstituteTonga 39.08.6%194616.6×11 -

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 Mathematical and Computational Methods, country by country

Is Mathematical and Computational Methods research growing?

Output in 2022-2025 was 26% higher than in 2018-2021, peaking in 2026. The fastest-growing topics are Mathematical and Computational Methods.

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 Mathematical and Computational Methods as a percentage of every work published that year, 0.00043% in 2024.

still counting0.0020%0.0040%0.0060%Mathematical and Computational Methods0.00090% in 202519801990200020102020

Fractional works of Mathematical and Computational Methods 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%Mathematical and Computational Methods9.7% 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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