OOIR: Observatory of International Research

Papers

(The median citation count of Numerical Mathematics-Theory Methods and Applications is 1. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-11-01 to 2024-11-01.)

Article	Citations
A Novel Numerical Approach to Time-Fractional Parabolic Equations with Nonsmooth Solutions	50
Spectral Analysis for Preconditioning of Multi-Dimensional Riesz Fractional Diffusion Equations	27
A Note on Parallel Preconditioning for the All-at-Once Solution of Riesz Fractional Diffusion Equations	25
A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems	22
Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations	15
The Variable-Step L1 Scheme Preserving a Compatible Energy Law for Time-Fractional Allen-Cahn Equation	15
A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation	15
Generalized Singular Value Decompositions for Tensors and Their Applications	9
A Unified Fast Memory-Saving Time-Stepping Method for Fractional Operators and Its Applications	9
Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy	8
Convergence of the Peaceman-Rachford Splitting Method for a Class of Nonconvex Programs	8
An Efficient Mapped WENO Scheme Using Approximate Constant Mapping	7
A Novel Class of Energy-Preserving Runge-Kutta Methods for the Korteweg-de Vries Equation	7
Two-Phase Image Segmentation by the Allen-Cahn Equation and a Nonlocal Edge Detection Operator	7
Fast Second-Order Evaluation for Variable-Order Caputo Fractional Derivative with Applications to Fractional Sub-Diffusion Equations	7
A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs	6
A Linear Hybridization of Dai-Yuan and Hestenes-Stiefel Conjugate Gradient Method for Unconstrained Optimization	5
On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors	5
Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments	5
A New Fixed-Time Dynamical System for Absolute Value Equations	5
On the Construction and Analysis of Finite Volume Element Schemes with Optimal $L^2$ Convergence Rate	4
On a Parabolic Sine-Gordon Model	4
Numerical Solution of a One-Dimensional Nonlocal Helmholtz Equation by Perfectly Matched Layers	4
Generating Layer-Adapted Meshes Using Mesh Partial Differential Equations	4
L1/Local Discontinuous Galerkin Method for the Time-Fractional Stokes Equation	4

On the Evolutionary Dynamics of the Cahn-Hilliard Equation with Cut-Off Mass Source	3
New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations	3
Explicit Hybrid Numerical Method for the Allen-Cahn Type Equations on Curved Surfaces	3
Accelerated Non-Overlapping Domain Decomposition Method for Total Variation Minimization	3
Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field	3
Efficient Hermite Spectral-Galerkin Methods for Nonlocal Diffusion Equations in Unbounded Domains	3
New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model	3
Phase-Field Modeling and Numerical Simulation for Ice Melting	3
The Virtual Element Method for an Elliptic Hemivariational Inequality with Convex Constraint	3
A Second-Order Semi-Implicit Method for the Inertial Landau-Lifshitz-Gilbert Equation	3
Quasi-Monte Carlo Sampling for Solving Partial Differential Equations by Deep Neural Networks	3
A Local Deep Learning Method for Solving High Order Partial Differential Equations	3
Variant of Greedy Randomized Gauss-Seidel Method for Ridge Regression	3
Mean-Square Approximation of Navier-Stokes Equations with Additive Noise in Vorticity-Velocity Formulation	3
Sparse Deep Neural Network for Nonlinear Partial Differential Equations	3
Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations	2
On Discontinuous and Continuous Approximations to Second-Kind Volterra Integral Equations	2
A Structure-Preserving JKO Scheme for the Size-Modified Poisson-Nernst-Planck-Cahn-Hilliard Equations	2
A High-Order Piecewise Quartic Spline Rule for Hadamard Integral and Its Application of the Cavity Scattering	2
An Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations	2
The Relation Between a Tensor and Its Associated Semi-Symmetric Form	2
Analysis of Anisotropic Nonlocal Diffusion Models: Well-Posedness of Fractional Problems for Anomalous Transport	2
Stability and Convergence Analyses of the FDM Based on Some L-Type Formulae for Solving the Subdiffusion Equation	2
A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model	2
Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise	2
A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations	2
Numerical Algorithm with Fourth-Order Spatial Accuracy for Solving the Time-Fractional Dual-Phase-Lagging Nanoscale Heat Conduction Equation	2
An Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection	2
Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems	2
The Direct Method of Lines for Forward and Inverse Linear Elasticity Problems of Composite Materials in Star-Shaped Domains	2
A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation	2
A Linearized Spectral-Galerkin Method for Three-Dimensional Riesz-Like Space Fractional Nonlinear Coupled Reaction-Diffusion Equations	2
Two-Step Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems	2
Discrete Approximation Scheme in Distributionally Robust Optimization	2
Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes	1
Efficient and Accurate Legendre Spectral Element Methods for One-Dimensional Higher Order Problems	1
A Novel Iterative Method to Find the Moore-Penrose Inverse of a Tensor with Einstein Product	1
A Dual-Horizon Nonlocal Diffusion Model and Its Finite Element Discretization	1
Finite Difference Method for Inhomogeneous Fractional Dirichlet Problem	1
An Accurate Numerical Scheme for Mean-Field Forward and Backward SDEs with Jumps	1
Strong Convergence of a Fully Discrete Scheme for Multiplicative Noise Driving SPDEs with Non-Globally Lipschitz Continuous Coefficients	1
Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator	1
Conservative Three-Level Linearized Finite Difference Schemes for the Fisher Equation and Its Maximum Error Estimates	1
An Acceleration Technique for the Augmented IIM for 3D Elliptic Interface Problems	1
Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System	1
Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough Coefficients	1
A General Cavitation Model for the Highly Nonlinear Mie-Grüneisen Equation of State	1
PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations	1
Artificial Boundary Conditions for Time-Fractional Telegraph Equation	1
An Improved Linearity-Preserving Cell-Centered Scheme for Nonlinear Diffusion Problems on General Meshes	1

Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes	1
A 2D Staggered Multi-Material ALE Code Using MOF Interface Reconstruction	1
On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion	1
The MFE-CFE-GFE Method for the Fully Coupled Quasi-Static Thermo-Poroelastic Problem	1
Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations	1
Stability and Convergence of the Integral-Averaged Interpolation Operator Based on $Q_1$-Element in $\mathbb{R}^n$	1
Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals	1
An Extended Two-Step Method for Inverse Eigenvalue Problems with Multiple Eigenvalues	1
A Physics-Informed Structure-Preserving Numerical Scheme for the Phase-Field Hydrodynamic Model of Ternary Fluid Flows	1
The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials	1
Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model	1
The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems	1
Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems	1
Symmetric-Adjoint and Symplectic-Adjoint Runge-Kutta Methods and Their Applications	1
Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain	1
Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media	1
HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network	1