1. Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schrödinger equations
   2025/12/18 by Ranocha, Hendrik, Ketcheson, David I. · 1 citation
   #65M12 #65M20 #65M60 #65M70 #FOS: Mathematics #Numerical Analysis (math.NA)
2. A Semi-Lagrangian Adaptive Rank (SLAR) Method for High-Dimensional Vlasov Dynamics
   2025/10/28 by Zheng, Nanyi, Sands, William A., Hayes, Daniel +2 · 3 citations
   #35Q83 #65F30 #65M70 #65Y20 #82D10 #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Plasma Physics (physics.plasm-ph)
3. High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperbolization
   2025/10/16 by Ranocha, Hendrik, Ketcheson, David I. · 2 citations
   #65M06 #65M12 #65M20 #65M60 #65M70 #FOS: Mathematics #Numerical Analysis (math.NA)
4. Recurrent Neural Operators: Stable Long-Term PDE Prediction
   2025/05/27 by Zhaoxiang Ye, Ye, Zaijun, C Zhang +3 · 2 citations
   Computer Science · #65M70 #68T07 #68U20 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Neural Networks and Applications #Numerical Analysis (math.NA)
5. An Adaptive-rank Approach with Greedy Sampling for Multi-scale BGK Equations
   2025/05/22 by Sands, William A., Qiu, Jing-Mei, Hayes, Daniel +1 · 3 citations
   #65F30 (secondary) #65M70 #65M85 (primary) #FOS: Mathematics #Numerical Analysis (math.NA)
6. Optimal error bounds on an exponential wave integrator Fourier spectral method for the logarithmic Schrödinger equation
   2024/12/22 by Weizhu Bao, Ying Ma, Bao, Weizhu +3 · 1 citation
   Engineering · Mathematics · #35Q55 #65M15 #65M70 #81Q05 #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in inverse problems
7. Analysis of the multi-dimensional semi-discrete Active Flux method using the Fourier transform
   2024/12/04 by Barsukow, Wasilij, Kern, Janina, Klingenberg, Christian +1 · 2 citations
   #35E15 #65M08 #65M20 #65M70 #FOS: Mathematics #Numerical Analysis (math.NA)
8. Explicit symmetric low-regularity integrators for the nonlinear Schrödinger equation
   2024/11/12 by Feng, Yue, Maierhofer, Georg, Wang, Chushan · 1 citation
   #35Q41 #35Q55 #65M12 #65M70 #FOS: Mathematics #Numerical Analysis (math.NA)
9. Frequency inversion method and device for malignant melanoma detection using RF/microwaves
   2024/10/04 by Beilina, Larisa, Eriksson, Anders, Neittaanmäki, Noora · 2 citations
   #65J22 #65K10 #65M32 #65M55 #65M60 #65M70 #FOS: Electrical engineering #FOS: Physical sciences #Medical Physics (physics.med-ph) #Signal Processing (eess.SP) #electronic engineering #information engineering
10. Constructing stable, high-order finite-difference operators on point clouds over complex geometries
    2024/09/01 by Jason E. Hicken, Hicken, Jason, Ge Yan +3 · 4 citations
    Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #65M06 #65M12 #65M70 #Data Management and Algorithms #FOS: Mathematics #Fibroblast Growth Factor Research #Fixed Point Theorems Analysis #Numerical Analysis (math.NA)
11. Entropy stable hydrostatic reconstruction schemes for shallow water systems
    2024/06/20 by Ersing, Patrick, Goldberg, Sven, Winters, Andrew R. · 1 citation
    #35L60 #65M12 #65M20 #65M70 #76M22 #86A05 #FOS: Mathematics #Numerical Analysis (math.NA)
12. On a class of multi-fidelity methods for the semiclassical Schrödinger equation with uncertainties
    2024/06/08 by Lin, Yiwen, Liu, Liu · 1 citation
    #35J10 #65M70 #FOS: Mathematics #Numerical Analysis (math.NA)
13. PETScML: Second-order solvers for training regression problems in Scientific Machine Learning
    2024/03/18 by Zampini, Stefano, Zerbinati, Umberto, Turkiyyah, George +1 · 1 citation
    #65K10 #65M70 #65Y05 #68T07 #D.2.m #FOS: Computer and information sciences #FOS: Mathematics #G.1.6 #G.4 #I.2.5 #J.2 #Machine Learning (cs.LG) #Mathematical Software (cs.MS) #Optimization and Control (math.OC)
14. Tensor Network Space-Time Spectral Collocation Method for Time Dependent Convection-Diffusion-Reaction Equations
    2024/02/28 by Dibyendu Adak, Duc P. Truong, Adak, Dibyendu +7 · 3 citations
    Engineering · Mathematics · #15A69 #35Q79 #65M70 #Differential Equations and Numerical Methods #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
15. Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations
    2024/02/26 by Lampert, Joshua, Ranocha, Hendrik · 3 citations
    #65M06 #65M20 #65M70 #FOS: Mathematics #Numerical Analysis (math.NA)
16. Low regularity estimates of the Lie-Totter time-splitting Fourier spectral method for the logarithmic Schrödinger equation
    2024/01/04 by Zhang, Xiaolong, Wang, Li-Lian · 1 citation
    #35Q55 #65M15 #65M70 #81Q05 #FOS: Mathematics #Numerical Analysis (math.NA)
17. Maximum principle preserving time implicit DGSEM for linear scalar hyperbolic conservation laws
    2023/10/30 by Milani, Riccardo, Renac, Florent, Ruel, Jean · 1 citation
    #65M12 #65M70 #76T10 #FOS: Mathematics #Numerical Analysis (math.NA)
18. A Novel Stochastic Interacting Particle-Field Algorithm for 3D Parabolic-Parabolic Keller-Segel Chemotaxis System
    2023/09/24 by Wang, Zhongjian, Xin, Jack, Zhang, Zhiwen · 5 citations
    #35K57 #65C35 #65M70 #65M75 #92C17 #FOS: Mathematics #Numerical Analysis (math.NA)
19. An L2-Error Estimate of Energy Stable Flux Reconstruction Method
    2023/09/07 by Lambert, Erwan, Nadarajah, Siva · 3 citations
    #65M15 #65M70 #76M10 #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
20. An improved local radial basis function method for solving small-strain elasto-plasticity
    2023/08/07 by Vuga, Gašper, Mavrič, Boštjan, Šarler, Božidar · 1 citation
    #65M70 #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA)
21. Error analysis of a first-order IMEX scheme for the logarithmic Schrödinger equation
    2023/06/28 by Li-Lian Wang, Wang, Lilian, Jingye Yan +3 · 1 citation
    Engineering · Mathematics · #35Q55 #65M15 #65M70 #81Q05 #Advanced Mathematical Physics Problems #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA) #Numerical methods for differential equations
22. Breaking quadrature exactness: A spectral method for the Allen--Cahn equation on spheres
    2023/05/08 by Hao-Ning Wu, Xiaoming Yuan, Wu, Hao-Ning +1 · 1 citation
    Earth and Planetary Sciences · Materials Science · #33C55 #35B50 #58J35 #65D32 #65M70 #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena #nanoparticles nucleation surface interactions
23. Algebraic calming for the 2D Kuramoto-Sivashinsky equations
    2023/04/20 by Enlow, Matthew, Larios, Adam, Wu, Jiahong · 2 citations
    #35A35 #35B65 #35K25 #35K58 #65M70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)
24. The Random Feature Method for Time-dependent Problems
    2023/04/14 by Jingrun Chen, Chen, Jingrun, E Weinan +3 · 4 citations
    Decision Sciences · Environmental Science · #65M20 #65M55 #65M70 #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Soil Geostatistics and Mapping
25. Symmetric-conjugate splitting methods for linear unitary problems
    2023/03/20 by Bernier, Joackim, Blanes, Sergio, Casas, Fernando +1 · 1 citation
    #65L05 #65L20 #65M70 #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)
26. Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations
    2023/02/01 by Feng, Yue, Maierhofer, Georg, Schratz, Katharina · 1 citation
    #35Q41 #35Q55 #65M15 #65M70 #FOS: Mathematics #Numerical Analysis (math.NA)
27. Eigenvalue Analysis and Applications of the Legendre Dual-Petrov-Galerkin Methods for Initial Value Problems
    2022/11/19 by Desong Kong, Kong, Desong, Jie Shen +5 · 1 citation
    Computer Science · Mathematics · #33C45 #65F15 #65L15 #65M70 #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
28. Conservative Evolution of Black Hole Perturbations with Time-Symmetric Numerical Methods
    2022/10/05 by Michael F. O’Boyle, O'Boyle, Michael F., C. Markakis +7 · 1 citation
    Engineering · Physics and Astronomy · #49K20 #49S05 #65M22 #65M25 #65M70 #70S10 #83-10 #83C25 #Astrophysical Phenomena and Observations #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Astrophysical Phenomena (astro-ph.HE) #Numerical Analysis (math.NA) #Pulsars and Gravitational Waves Research #Superconducting Materials and Applications
29. Bridging the gap: symplecticity and low regularity in Runge-Kutta resonance-based schemes
    2022/05/10 by Maierhofer, Georg, Schratz, Katharina · 2 citations
    #35Q53 #65M12 #65M70 #FOS: Mathematics #Numerical Analysis (math.NA)
30. The hydrodynamics of a twisting, bending, inextensible fiber in Stokes flow
    2022/01/11 by Ondrej Maxian, Brennan Sprinkle, Maxian, Ondrej +5 · 2 citations
    Engineering · Physics and Astronomy · #65M70 #65R20 #74F10 #76Z05 #Biomimetic flight and propulsion mechanisms #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Lattice Boltzmann Simulation Studies #Micro and Nano Robotics #Numerical Analysis (math.NA)

more