Numerical Mathematics-Theory Methods and Applications

Papers
(The median citation count of Numerical Mathematics-Theory Methods and Applications is 0. 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 2021-05-01 to 2025-05-01.)
ArticleCitations
A Priori Error Estimate of Nonconforming Virtual Element Method for Convection Dominated Diffusion Equation32
A Generalized Selectively Relaxed Matrix Splitting Preconditioning Strategy for Three-Dimensional Flux-Limited Multi-Group Radiation Diffusion Equations28
Symmetric-Adjoint and Symplectic-Adjoint Runge-Kutta Methods and Their Applications20
L1/Local Discontinuous Galerkin Method for the Time-Fractional Stokes Equation20
Analysis and Optimal Control of a System of Hemivariational Inequalities Arising in Non-Stationary Navier-Stokes Equation with Thermal Effects18
Character Modelling with Sketches and ODE-Based Shape Creation9
A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation9
On Discontinuous and Continuous Approximations to Second-Kind Volterra Integral Equations8
New Extrapolation Modulus-based Economical Cascadic Multigrid Method for Variational Inequality Problems with Nonlinear Source Terms7
New Log Basis Functions with a Scaling Factor and Their Applications7
Space-Time Decomposition of Kalman Filter5
Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field5
Fusing Infrared and Visible Images via a First-Order Model5
Sparse Deep Neural Network for Nonlinear Partial Differential Equations5
PI-VEGAN: Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations4
Low Rank and Total Variation Based Two-Phase Method for Image Deblurring with Salt-and-Pepper Impulse Noise4
Enhancing RBF-FD Efficiency for Highly Non-Uniform Node Distributions via Adaptivity4
Convergence Analysis of a Quasi-Monte Carlo-Based Deep Learning Algorithm for Solving Partial Differential Equations4
A Study on CFL Conditions for the DG Solution of Conservation Laws on Adaptive Moving Meshes3
Efficient Hermite Spectral-Galerkin Methods for Nonlocal Diffusion Equations in Unbounded Domains3
HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network3
Green Function Method for Quantum Transport Based on the Generalized Fourier Transform3
Manifold Triangular Mesh Editing Based on Finite Differences and Fourier Series3
An Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection3
Numerical Algorithm with Fourth-Order Spatial Accuracy for Solving the Time-Fractional Dual-Phase-Lagging Nanoscale Heat Conduction Equation2
On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion2
Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model2
The Discontinuous Galerkin Method by Divergence-Free Patch Reconstruction for Stokes Eigenvalue Problems2
A BDF2-SSAV Numerical Scheme with Fourier-Spectral Method for a Droplet Thin Film Coarsening Model2
Convergence of Weak Galerkin Finite Element Method for Second Order Linear Wave Equation in Heterogeneous Media2
A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations2
Stability and Error Analysis of SAV Semi-Discrete Scheme for Cahn-Hilliard-Navier-Stokes Model2
A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows2
Analysis of Deep Ritz Methods for Semilinear Elliptic Equations2
Projection Improved SPAI Preconditioner for FGMRES2
A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations2
A Novel Class of Energy-Preserving Runge-Kutta Methods for the Korteweg-de Vries Equation2
Finite Difference Method for Inhomogeneous Fractional Dirichlet Problem1
An Efficient Mapped WENO Scheme Using Approximate Constant Mapping1
A Second-Order Semi-Implicit Method for the Inertial Landau-Lifshitz-Gilbert Equation1
Analysis and Efficient Implementation of Quadratic Spline Collocation ADI Methods for Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations1
Two Dynamical Models Based on Projection Operator for Solving the System of Absolute Value Equations Associated with Second-Order Cone1
New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model1
Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations1
A Fast Compact Block-Centered Finite Difference Method on Graded Meshes for Time-Fractional Reaction-Diffusion Equations and Its Robust Analysis1
Fourier Convergence Analysis for a Fokker-Planck Equation of Tempered Fractional Langevin-Brownian Motion1
Richardson Extrapolation of the Euler Scheme for Backward Stochastic Differential Equations1
Robust Globally Divergence-Free Weak Galerkin Methods for Stationary Incompressible Convective Brinkman-Forchheimer Equations1
Splitting ADI Scheme for Fractional Laplacian Wave Equations1
Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation1
An Efficient Variational Model for Multiplicative Noise Removal1
Convergence Analysis of Split-Douglas-Rachford Algorithm and a Novel Preconditioned ADMM with an Improved Condition1
A Stabilized Physics Informed Neural Networks Method for Wave Equations1
A Structure-Preserving JKO Scheme for the Size-Modified Poisson-Nernst-Planck-Cahn-Hilliard Equations1
Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator1
Penalized Schemes for Hamilton-Jacobi-Bellman Quasi-Variational Inequalities Arising in Regime Switching Utility Maximization with Optimal Stopping1
The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials1
A Convergence Analysis of a Structure-Preserving Gradient Flow Method for the All-Electron Kohn-Sham Model1
Noise Robust Physics-Informed Generative Adversarial Networks for Solving Stochastic Differential Equations1
A Local Deep Learning Method for Solving High Order Partial Differential Equations1
Convergent and Orthogonality Preserving Schemes for Approximating the Kohn-Sham Orbitals1
Convergence Analysis of OT-Flow for Sample Generation1
A Robust Hybrid Spectral Method for Nonlocal Problems with Weakly Singular Kernels1
A Divergence-Free $P_k$ CDG Finite Element for the Stokes Equations on Triangular and Tetrahedral Meshes1
Finding Symmetry Groups of Some Quadratic Programming Problems0
Numerical Solution of a One-Dimensional Nonlocal Helmholtz Equation by Perfectly Matched Layers0
A Lagrangian Discontinuous Galerkin Scheme for the Compressible Euler Equations on Unstructured Triangular Meshes0
Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters0
The Direct Discontinuous Galerkin Method with Explicit-Implicit-Null Time Discretizations for Nonlinear Diffusion Equations0
MC-Nonlocal-PINNs: Handling Nonlocal Operators in PINNs via Monte Carlo Sampling0
Variable $s$-Step Technique for New Conjugate Residual Algorithms for Solving Non-Square Linear Systems Arising in Control Problems0
Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System0
Application of Adapted-Bubbles to the Helmholtz Equation with Large Wavenumbers in 2D0
On Polar Decomposition of Tensors with Einstein Product and a Novel Iterative Parametric Method0
Multi-Dimensional Image Recovery via SelfSupervised Nonlinear Transform Based a Three-Directional Tensor Nuclear Norm0
On the Criteria for Online Updating of Basis Functions for Model Order Reduction Techniques0
An Extended Two-Step Method for Inverse Eigenvalue Problems with Multiple Eigenvalues0
An Alternating Direction Method of Multipliers for Inverse Lithography Problem0
Stability of Spike Solutions to the Fractional Gierer-Meinhardt System in a One-Dimensional Domain0
Artificial Boundary Conditions for Time-Fractional Telegraph Equation0
Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes0
Frontal Slice Approaches for Tensor Linear Systems0
New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations0
An Extended Courant Element on a Polytope with Application in Approximating an Obstacle Problem0
Absorbing Interface Conditions for the Simulation of Wave Propagation on Non-Uniform Meshes0
Linearized Double-Shock Approximate Riemann Solver for Augmented Linear Elastic Solid0
A Finite Volume Simple WENO Scheme for Convection-Diffusion Equations0
Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise0
Long Time Energy and Kinetic Energy Conservations of Exponential Integrators for Highly Oscillatory Conservative Systems0
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for a Liquid Thin Film Coarsening Model0
Finite Element Error Estimation for Parabolic Optimal Control Problems with Pointwise Observations0
A New Fixed-Time Dynamical System for Absolute Value Equations0
Numerical Solution of Partial Differential Equations in Arbitrary Shaped Domains Using Cartesian Cut-Stencil Finite Difference Method. Part II: Higher-Order Schemes0
Greedy Kaczmarz Algorithm Using Optimal Intermediate Projection Technique for Coherent Linear Systems0
Unconditional Convergence of Linearized TL1 Difference Methods for a Time-Fractional Coupled Nonlinear Schrödinger System0
A Stabilizer Free Weak Galerkin Finite Element Method for Elliptic Equation with Lower Regularity0
On the Recovery of Source Term for Fractional Evolution PDEs by MC-fPINNs0
Multi-Phase Segmentation Using Modified Complex Cahn-Hilliard Equations0
A Nonlocal Stokes System with Volume Constraints0
A Unified Fast Memory-Saving Time-Stepping Method for Fractional Operators and Its Applications0
Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations0
The Relation Between a Tensor and Its Associated Semi-Symmetric Form0
The MFE-CFE-GFE Method for the Fully Coupled Quasi-Static Thermo-Poroelastic Problem0
Two-Phase Image Segmentation by the Allen-Cahn Equation and a Nonlocal Edge Detection Operator0
Efficiently Training Physics-Informed Neural Networks via Anomaly-Aware Optimization0
A Dual-Horizon Nonlocal Diffusion Model and Its Finite Element Discretization0
An Efficient Cartesian Grid-Based Method for Scattering Problems with Inhomogeneous Media0
ODE-Based Multistep Schemes for Backward Stochastic Differential Equations0
Maximum-Principle-Preserving High-Order Conservative Difference Schemes for Convection-Dominated Diffusion Equations0
Non-Local and Fully Connected Tensor Network Decomposition for Remote Sensing Image Denoising0
A Convergence Study of SGD-Type Methods for Stochastic Optimization0
Analysis of Anisotropic Nonlocal Diffusion Models: Well-Posedness of Fractional Problems for Anomalous Transport0
Geometric Design of Letters in Times Roman Font via RBF Meshless Collocation Method0
The Direct Method of Lines for Forward and Inverse Linear Elasticity Problems of Composite Materials in Star-Shaped Domains0
Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli0
R-Adaptive DeepONet: Learning Solution Operators for PDEs with Discontinuous Solutions Using an R-Adaptive Strategy0
The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems0
A Third-Order Implicit-Explicit Runge-Kutta Method for Landau-Lifshitz Equation with Arbitrary Damping Parameters0
Divergence-Free Virtual Element Method for the Stokes Equations with Damping on Polygonal Meshes0
Spectral Analysis for Preconditioning of Multi-Dimensional Riesz Fractional Diffusion Equations0
Multidomain Hybrid Direct DG and Central Difference Methods for Viscous Terms in Hyperbolic-Parabolic Equations0
Finding Cheeger Cuts via 1-Laplacian of Graphs0
A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems0
Error Analysis of the Mixed Residual Method for Elliptic Equations0
An Adaptive Physics-Informed Neural Network with Two-Stage Learning Strategy to Solve Partial Differential Equations0
An Accurate Numerical Scheme for Mean-Field Forward and Backward SDEs with Jumps0
New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications0
Numerical Integration Formulas for Hypersingular Integrals0
Error Analysis of the Deep Mixed Residual Method for High-order Elliptic Equations0
Two-Step Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems0
On Lagrange-Projection Schemes for Shallow Water Flows over Movable Bottom with Suspended and Bedload Transport0
The Stabilized Finite Element Method for the Cahn-Hilliard Phase-Field Model of Diblock Copolymers on Evolving Surfaces0
A Riemannian Inertial Mann Algorithm for Nonexpansive Mappings on Hadamard Manifolds0
A Physics-Informed Structure-Preserving Numerical Scheme for the Phase-Field Hydrodynamic Model of Ternary Fluid Flows0
Convergence of a Generalized Primal-Dual Algorithm with an Improved Condition for Saddle Point Problems0
The Variable-Step L1 Scheme Preserving a Compatible Energy Law for Time-Fractional Allen-Cahn Equation0
Learning Epidemic Trajectories Through Kernel Operator Learning: From Modelling to Optimal Control0
High Order Mixed Finite Elements with Mass Lumping for Elasticity on Triangular Grids0
L1 Schemes for Time-Fractional Differential Equations: A Brief Survey and New Development0
A Modularized Algorithmic Framework for Interface Related Optimization Problems Using Characteristic Functions0
Stability and Convergence of the Integral-Averaged Interpolation Operator Based on $Q_1$-Element in $\mathbb{R}^n$0
An Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three Dimensions0
Conservative Three-Level Linearized Finite Difference Schemes for the Fisher Equation and Its Maximum Error Estimates0
Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment0
A Variant Modified Skew-Normal Splitting Iterative Method for Non-Hermitian Positive Definite Linear Systems0
A Posteriori Error Analysis of a $P_2$-CDG Space-Time Finite Element Method for the Wave Equation0
A Novel Iterative Method to Find the Moore-Penrose Inverse of a Tensor with Einstein Product0
Energy-Preserving Parareal-RKN Algorithms for Hamiltonian Systems0
Fast Second-Order Evaluation for Variable-Order Caputo Fractional Derivative with Applications to Fractional Sub-Diffusion Equations0
Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes0
Error Analysis for Empirical Risk Minimization over Clipped ReLU Networks in Solving Linear Kolmogorov Partial Differential Equations0
Numerical Continuation and Bifurcation for Differential Geometric PDEs0
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