Leaderboards/Numerical methods for differential equations

Numerical methods for differential equations

Last updated July 7, 2026

Rising Stars

New and hot

Rising Stars Researchers

1
J. Klappert
RWTH Aachen University
2
Daniel A. Messenger
Los Alamos National Laboratory
3
Nicolás Faedo
National University of Ireland, Maynooth
4
Qing Cheng
Tongji University
5
Rudy Geelen
Texas A&M University System
6
Sudarshan Santra
Indian Institute of Science Bangalore
7
Meiyan Zou
Wuhan University of Technology
8
Harsh Sharma
University of California San Diego
9
Nicolás Espitia
Université de Lille
10
Hind Sweis
University of Jordan

Rising Stars Papers

1
Experimental and numerical investigation of gap resonances between side-by-side fixed barges under beam sea excitation
Ocean Engineering|2024
48 cit.
2
Existence, uniqueness, and galerkin shifted Legendre's approximation of time delays integrodifferential models by adapting the Hilfer fractional attitude
Heliyon|2024
31 cit.
3
Learning physics-based reduced-order models from data using nonlinear manifolds
Chaos An Interdisciplinary Journal of Nonlinear Science|2024
30 cit.
4
Well-posedness analysis and pseudo-Galerkin approximations using Tau Legendre algorithm for fractional systems of delay differential models regarding Hilfer (α,β)-framework set
PLoS ONE|2024
22 cit.
5
Lagrangian operator inference enhanced with structure-preserving machine learning for nonintrusive model reduction of mechanical systems
Computer Methods in Applied Mechanics and Engineering|2024
21 cit.
6
Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems
Physica D Nonlinear Phenomena|2024
21 cit.
7
Analysis of a higher-order scheme for multi-term time-fractional integro-partial differential equations with multi-term weakly singular kernels
Numerical Algorithms|2024
19 cit.
8
Development of a coupled time-domain model for complexly moored multi-body system with application in catamaran float-over deck installation
Marine Structures|2025
16 cit.
9
Simultaneous space–time Hermite wavelet method for time-fractional nonlinear weakly singular integro-partial differential equations
Communications in Nonlinear Science and Numerical Simulation|2024
13 cit.
10
Towards modelling and control strategies for hybrid wind-wave energy converters: Challenges and opportunities
Renewable and Sustainable Energy Reviews|2025
10 cit.

Emerging Leaders

Gaining momentum

Emerging Leaders Researchers

1
Omar Bazighifan
University of Aden
2
Johann Usovitsch
Humboldt-Universität zu Berlin
3
Ioannis Dassios
Aristotle University of Thessaloniki
4
Wenlin Qiu
Hunan Normal University
5
Ali Muhib
Jadara University
6
Zhong-Zhou Lan
Inner Mongolia University of Finance and Economics
7
Chenyu Wang
Tsinghua University
8
Marion Chandesris
Laboratoire d’Innovation pour les Technologies des Énergies Nouvelles et les nanomatériaux
9
Dongfang Li
Nofima
10
Diego Tapias
University of Göttingen

Emerging Leaders Papers

1
Enhancing catalytic activity of gold nanoparticles in a standard redox reaction by investigating the impact of AuNPs size, temperature and reductant concentrations
Scientific Reports|2023
101 cit.
2
Conservative Black Hole Scattering at Fifth Post-Minkowskian and First Self-Force Order
Physical Review Letters|2024
89 cit.
3
Emergence of Calabi–Yau manifolds in high-precision black-hole scattering
Nature|2025
61 cit.
4
Efficient alternating direction implicit numerical approaches for multi-dimensional distributed-order fractional integro differential problems
Computational and Applied Mathematics|2022
45 cit.
5
Semirational rogue waves of the three coupled higher-order nonlinear Schrödinger equations
Applied Mathematics Letters|2023
45 cit.
6
Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions
Mathematics|2022
44 cit.
7
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg" display="inline" id="d1e413"><mml:mi>N</mml:mi></mml:math>-soliton solutions, Bäcklund transformation and Lax Pair for a generalized variable-coefficient cylindrical Kadomtsev–Petviashvili equation
Applied Mathematics Letters|2024
40 cit.
8
Multi-soliton solutions, breather-like and bound-state solitons for complex modified Korteweg–de Vries equation in optical fibers
Chinese Physics B|2024
38 cit.
9
Numerical investigation of generalized tempered-type integrodifferential equations with respect to another function
Fractional Calculus and Applied Analysis|2023
35 cit.
10
Multiple Soliton Asymptotics in a Spin-1 Bose–Einstein Condensate
Chinese Physics Letters|2024
35 cit.

Current Senior Leaders

Established & currently active

Current Senior Leaders Researchers

1
Kenneth V. Price
Universidade de Marília
2
Chi‐Wang Shu
Brown University
3
T. E. Simos
Technical University of Crete
4
Gerhard Wanner
Ludwig-Maximilians-Universität München
5
Neville J. Ford
University of Chester
6
Linda Petzold
University of California, Santa Barbara
7
Robert L. Taylor
University of California, Berkeley
8
Alexander Ostermann
Universität Innsbruck
9
L. D. Marini
University of Minnesota
10
Theodore E. Simos
Democritus University of Thrace

Current Senior Leaders Papers

1
Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces
Journal of Global Optimization|1997
28.7k cit.
2
Efficient Implementation of Weighted ENO Schemes
Journal of Computational Physics|1996
6.5k cit.
3
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics|1989
4.9k cit.
4
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics|1988
4.7k cit.
5
Solving ordinary differential equations I. nonstiff problems
Mathematics and Computers in Simulation|1987
4.1k cit.
6
Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces
Unknown Journal|2004
3.4k cit.
7
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis|2002
3.2k cit.
8
Analysis of Fractional Differential Equations
Journal of Mathematical Analysis and Applications|2002
3.2k cit.
9
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation|1998
2.5k cit.
10
Improved numerical dissipation for time integration algorithms in structural dynamics
Earthquake Engineering & Structural Dynamics|1977
2.4k cit.

Reagents for Numerical methods for differential equations

Citation-validated products used in this field

🔥 Trending

Gaining adoption fast

⭐ Top Rated

Best all-around

Cell Signaling TechnologyEvidence 66

Ubiquityl-Histone H2B (Lys120) (D11) Rabbit Monoclonal Antibody (PE Conjugate)

#86653$493
View Evidence →
Cell Signaling TechnologyEvidence 66

ERp44 (D17A6) Rabbit Monoclonal Antibody (BSA and Azide Free)

#89694$865
View Evidence →
Cell Signaling TechnologyEvidence 64

LEF1 (D6J2W) Rabbit Monoclonal Antibody

#76010$161,351
View Evidence →

🌟 All-Time

Most validated

Cell Signaling TechnologyEvidence 64

GPR52 (E9D8W) Rabbit Monoclonal Antibody (BSA and Azide Free)

#65216$865
View Evidence →
Cell Signaling TechnologyEvidence 63

AFP (F2E9D) Rabbit Monoclonal Antibody

#35190$178,415
View Evidence →
Cell Signaling TechnologyEvidence 62

Bcl-3 (E2M6N) Rabbit Monoclonal Antibody

#90776$161,351
View Evidence →