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 2020-03-01 to 2024-03-01.)

Article	Citations
A Novel Numerical Approach to Time-Fractional Parabolic Equations with Nonsmooth Solutions	40
A Note on Parallel Preconditioning for the All-at-Once Solution of Riesz Fractional Diffusion Equations	23
A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems	18
Spectral Analysis for Preconditioning of Multi-Dimensional Riesz Fractional Diffusion Equations	18
Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations	11
Convergence Analysis of a Numerical Scheme for the Porous Medium Equation by an Energetic Variational Approach	10
The Variable-Step L1 Scheme Preserving a Compatible Energy Law for Time-Fractional Allen-Cahn Equation	9
A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation	9
Finite Element Approximation of Space Fractional Optimal Control Problem with Integral State Constraint	8
One-Step Hybrid Block Method Containing Third Derivatives and Improving Strategies for Solving Bratu’s and Troesch’s Problems	8
Convergence of the Peaceman-Rachford Splitting Method for a Class of Nonconvex Programs	7
Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy	7
The Generalized Order Tensor Complementarity Problems	7
Error Analysis of SAV Finite Element Method to Phase Field Crystal Model	7
A Unified Fast Memory-Saving Time-Stepping Method for Fractional Operators and Its Applications	6
A Novel Class of Energy-Preserving Runge-Kutta Methods for the Korteweg-de Vries Equation	6
Fast Second-Order Evaluation for Variable-Order Caputo Fractional Derivative with Applications to Fractional Sub-Diffusion Equations	6
Effect of Space Dimensions on Equilibrium Solutions of Cahn--Hilliard and Conservative Allen--Cahn Equations	6
An Efficient Mapped WENO Scheme Using Approximate Constant Mapping	6
Numerical Analysis of a Dynamic Contact Problem with History-Dependent Operators	5
A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs	5
A Dynamical Method for Solving the Obstacle Problem	5
Improved 3D Surface Reconstruction via the Method of Fundamental Solutions	5
A Two-Grid Algorithm of Fully Discrete Galerkin Finite Element Methods for a Nonlinear Hyperbolic Equation	5
Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments	5

Numerical Investigation of Sound Generation due to Laminar Flow Past Elliptic Cylinders	5
Two-Grid Finite Element Method with Crank-Nicolson Fully Discrete Scheme for the Time-Dependent Schrodinger Equation	5
Two-Phase Image Segmentation by the Allen-Cahn Equation and a Nonlocal Edge Detection Operator	5
On Nonnegative Solution of Multi-Linear System with Strong $\mathcal{M}_z$-Tensors	4
Generalized Singular Value Decompositions for Tensors and Their Applications	4
Solution Remapping Technique to Accelerate Flow Convergence for Finite Volume Methods Applied to Shape Optimization Design	4
Fast Evaluation of Linear Combinations of Caputo Fractional Derivatives and Its Applications to Multi-Term Time-Fractional Sub-Diffusion Equations	4
Numerical Solution of a One-Dimensional Nonlocal Helmholtz Equation by Perfectly Matched Layers	4
The Conservation and Convergence of Two Finite Difference Schemes for KdV Equations with Initial and Boundary Value Conditions	3
A Linear Hybridization of Dai-Yuan and Hestenes-Stiefel Conjugate Gradient Method for Unconstrained Optimization	3
On a Parabolic Sine-Gordon Model	3
A Well-Conditioned, Nonconforming Nitsche's Extended Finite Element Method for Elliptic Interface Problems	3
A Vertex-Centered and Positivity-Preserving Finite Volume Scheme for Two-Dimensional Three-Temperature Radiation Diffusion Equations on General Polygonal Meshes	3
A Stabilized Low Order Finite Element Method for Three Dimensional Elasticity Problems	3
A High-Order Kernel-Free Boundary Integral Method for Incompressible Flow Equations in Two Space Dimensions	3
A Continuous-Stage Modified Leap-Frog Scheme for High-Dimensional Semi-Linear Hamiltonian Wave Equations	3
Accelerated Non-Overlapping Domain Decomposition Method for Total Variation Minimization	2
Mean-Square Approximation of Navier-Stokes Equations with Additive Noise in Vorticity-Velocity Formulation	2
L1/Local Discontinuous Galerkin Method for the Time-Fractional Stokes Equation	2
Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise	2
A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation	2
Effect of Flux Evaluation Methods on the Resolution and Robustness of the Two-Step Finite-Difference WENO Scheme	2
Newton Linearized Methods for Semilinear Parabolic Equations	2
Mathematical Modeling and Simulation of Antibubble Dynamics	2
On Discontinuous and Continuous Approximations to Second-Kind Volterra Integral Equations	2
Multidomain Legendre-Galerkin Least-Squares Method for Linear Differential Equations with Variable Coefficients	2
On the Construction and Analysis of Finite Volume Element Schemes with Optimal $L^2$ Convergence Rate	2
A Fast Symmetric Alternating Direction Method of Multipliers	2
A High-Order Piecewise Quartic Spline Rule for Hadamard Integral and Its Application of the Cavity Scattering	2
A Linearized Spectral-Galerkin Method for Three-Dimensional Riesz-Like Space Fractional Nonlinear Coupled Reaction-Diffusion Equations	2
New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations	2
An Adaptive Nonmonotone Projected Barzilai-Borwein Gradient Method with Active Set Prediction for Nonnegative Matrix Factorization	2
Explicit Hybrid Numerical Method for the Allen-Cahn Type Equations on Curved Surfaces	2
Phase-Field Modeling and Numerical Simulation for Ice Melting	2
Stability and Convergence Analyses of the FDM Based on Some L-Type Formulae for Solving the Subdiffusion Equation	2
A Second-Order Semi-Implicit Method for the Inertial Landau-Lifshitz-Gilbert Equation	2
A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations	2
Generating Layer-Adapted Meshes Using Mesh Partial Differential Equations	2
On the Evolutionary Dynamics of the Cahn-Hilliard Equation with Cut-Off Mass Source	2
A Simple Semi-Implicit Scheme for Partial Differential Equations with Obstacle Constraints	2
Variant of Greedy Randomized Gauss-Seidel Method for Ridge Regression	2
Low Regularity Error Analysis for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems	2
Quasi-Monte Carlo Sampling for Solving Partial Differential Equations by Deep Neural Networks	1
Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations	1
A New Iteration and Preconditioning Method for Elliptic PDE-Constrained Optimization Problems	1
Discrete Approximation Scheme in Distributionally Robust Optimization	1
A Finite Volume Scheme for Savage-Hutter Equations on Unstructured Grids	1
Sparse Deep Neural Network for Nonlinear Partial Differential Equations	1
An Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations	1
An Improved Hybrid Adjoint Method in External Aerodynamics Using Variational Technique for the Boundary Integral Based Optimal Objective Function Gradient	1

A Multiple Scalar Auxiliary Variables Approach to the Energy Stable Scheme of the Moving Contact Line Problem	1
A 2D Staggered Multi-Material ALE Code Using MOF Interface Reconstruction	1
A Local Deep Learning Method for Solving High Order Partial Differential Equations	1
Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough Coefficients	1
A General Cavitation Model for the Highly Nonlinear Mie-Gruneisen Equation of State	1
Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator	1
Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field	1
A Structure-Preserving JKO Scheme for the SizeModified Poisson-Nernst-Planck-Cahn-Hilliard Equations	1
Parallel Smoothed Aggregation Multilevel Schwarz Preconditioned Newton-Krylov Algorithms for Poisson-Boltzmann Problems	1
An Acceleration Technique for the Augmented IIM for 3D Elliptic Interface Problems	1
Finite Difference Method for Inhomogeneous Fractional Dirichlet Problem	1
Superconvergence of the Composite Rectangle Rule for Computing Hypersingular Integral on Interval	1
Analysis of Anisotropic Nonlocal Diffusion Models: Well-Posedness of Fractional Problems for Anomalous Transport	1
Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System	1
Highly Accurate Numerical Schemes for Stochastic Optimal Control Via FBSDEs	1
Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations	1
A Robust Hybrid Spectral Method for Nonlocal Problems with Weakly Singular Kernels	1
New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model	1
Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes	1
A New Fixed-Time Dynamical System for Absolute Value Equations	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
Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain	1
The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials	1
Numerical Algorithm with Fourth-Order Spatial Accuracy for Solving the TimeFractional Dual-Phase-Lagging Nanoscale Heat Conduction Equation	1
An Improved Linearity-Preserving Cell-Centered Scheme for Nonlinear Diffusion Problems on General Meshes	1
Decoupled Mixed Element Methods for Fourth Order Elliptic Optimal Control Problems with Control Constraints	1
Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems	1
An Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection	1
Strong Convergence of a Fully Discrete Scheme for Multiplicative Noise Driving SPDEs with Non-Globally Lipschitz Continuous Coefficients	1
PPIFE Method with Non-Homogeneous Flux Jump Conditions and Its Efficient Numerical Solver for Elliptic Optimal Control Problems with Interfaces	1
Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part I: Concepts and Fundamentals	1
Auxiliary Equations Approach for the Stochastic Unsteady Navier--Stokes Equations with Additive Random Noise	1
On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion	1
The Virtual Element Method for an Elliptic Hemivariational Inequality with Convex Constraint	1