On the Construction and Comparison of Difference Schemes

No abstract is available for this paper.

• Publication year

  1968

• Venue

  SIAM Journal on Numerical Analysis

• Publication date

  1968-09-01

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1137/0705041
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Second-order numerical advection

  1967cited by this paper
• A Runge-Kutta for all Seasons

  1967cited by this paper
• FINITE DIFFERENCE CALCULATIONS FOR HYDRODYNAMIC FLOWS CONTAINING DISCONTINUITIES

  1965cited by this paper
• Accurate partial difference methods

  1964cited by this paper
• Difference schemes for hyperbolic equations with high order of accuracy

  1964cited by this paper
• Numerical methods in multidimensional shocked flows

  1964influential reference
• Accurate partial difference methods I: Linear cauchy problems

  1963cited by this paper
• Discrete Variable Methods in Ordinary Differential Equations

  1962cited by this paper
• Systems of conservation laws

  1960cited by this paper

• Test-time Generalization for Physics through Neural Operator Splitting

  2026cites this paper
• Internal Trajectories and Observation Effects in Langevin Splitting Schemes

  2026cites this paper
• Propagation characteristics of H2–air detonations in double-bend ducts

  2026cites this paper
• Simulation of ultrafast photonic circuits via nonlinear Schrödinger dynamics and quantum detector modeling

  2026cites this paper
• An equation for the curvature probability density function of instantaneous flame fronts

  2026cites this paper
• Reduced Kinetic Model for ns-DBD Plasma Actuators at Atmospheric Pressure

  2026cites this paper
• Turbulent hydrogen premixed flames at high pressure and high temperature

  2026cites this paper
• Immersed boundary conditions using the spectral difference method applied to turbulent flows over rough surfaces

  2026cites this paper
• XFluids: A unified cross-architecture high performance heterogeneous reacting flows simulation solver

  2026cites this paper
• Tensor Network Compression for Fully Spectral Vlasov-Poisson Simulation

  2026cites this paper
• A sixth-order compact time-splitting Fourier pseudospectral method

  2026cites this paper
• A novel shape transformation method via the nonlocal modified Allen-Cahn model: Analysis and numerical simulations*

  2026cites this paper
• A hybrid implicit-explicit time integration for stiff chemically reacting flows based on adaptive component-splitting method

  2026cites this paper
• Comparison of forcing models in the discrete unified gas kinetic scheme for compressible turbulence

  2026cites this paper
• Simulations of rim stabilized edge flames at atmospheric and high pressures using a p-adaptive spectral difference method

  2026cites this paper
• Machine-learning graph convolutional electronic propagators.

  2026cites this paper
• Quintic Uniform Algebraic Hyperbolic tension B-spline collocation method for soving multi-dimensional Kuramoto-Tsuzuki equation

  2026cites this paper
• A stable least squares finite difference-based fractional step lattice Boltzmann method for incompressible flows

  2026cites this paper
• Capturing Secondary Kinetic Instabilities in Three-Dimensional Dayside Reconnection Using an Improved Gradient-Based Closure

  2026cites this paper
• A cross-dimensional discrete Boltzmann framework for fluid dynamics

  2026cites this paper
• Quantum circuit design from a retraction-based Riemannian optimization framework

  2026cites this paper
• SOON: Symmetric Orthogonal Operator Network for Global Subseasonal-to-Seasonal Climate Forecasting

  2026cites this paper
• YuriiFormer: A Suite of Nesterov-Accelerated Transformers

  2026cites this paper
• GenCP: Towards Generative Modeling Paradigm of Coupled Physics

  2026cites this paper
• From Atoms to Neuronal Spikes: A Multiscale Simulation Framework

  2026cites this paper
• Partition-of-unity flow-based solver for kinetic plasma simulations

  2026cites this paper
• Unreacted pocket closure and jet flame formation in H <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si91.svg" display="inline" id="d1e855"> <mml:msub> <mml:mrow/> <mml:mrow>

  2026cites this paper
• Full-fluid modelling of rotating plasma instabilities in Penning-like configurations

  2026cites this paper
• Spatial Characteristics of Entropy Generation in Intrinsically Unstable Laminar Premixed Flames

  2026cites this paper
• An innovative meshless approach for solving 2D Allen-Cahn equations using the RBF-compact finite difference method

  2026cites this paper
• Geologic hydrogen as an emerging fuel: experimental insights, thermodynamics, kinetics, and reactive transport modeling

  2026cites this paper
• Plasma kinetics: Anomalous transport process in a hollow cathode plume

  2026cites this paper
• Thermodynamically consistent phase-field modeling and numerical simulation for two-phase fluid-solid dynamics

  2026cites this paper
• A hierarchical splitting approach for N-split differential equations

  2026influential citation
• Quantum computing of the nonlinear Schr\"odinger equation via measurement-induced potential reconstruction

  2026cites this paper
• Numerical Simulations of Supersonic Multi-Component and Reacting Flows: Towards Combustion in a Supersonic Cavity

  2026cites this paper
• Stability and convergence of high-order WENO-OS scheme for the Allen-Cahn equation

  2026cites this paper
• A Discontinuous Galerkin Spectral Element Method for Chemically Reacting Flows

  2026cites this paper
• BEACONS: Bounded-Error, Algebraically-Composable Neural Solvers for Partial Differential Equations

  2026cites this paper
• A semi-implicit method for the finite-rate chemistry integration in numerical simulations of combustion: Application to highly compressible flows

  2026cites this paper
• Error Estimates of the Fourier Collocation Combined Strang Splitting Method for Benjamin-Bona-Mahony Type Equations

  2026cites this paper
• The dynamics of oblique detonation waves in non-uniform inflows: Flame structure and stability

  2026cites this paper
• Clustered Projection Pursuit Adaptation (CPPA) for Combustion Chemistry

  2026cites this paper
• Multiscale Simulation Monte Carlo Method: Linking Spatiotemporal Discretization Error Analysis to Algorithmic Development

  2026cites this paper
• PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting

  2026cites this paper
• Extending numerical simulations in SIMPSON: Electron paramagnetic resonance, dynamic nuclear polarisation, propagator splitting, pulse transients, and quadrupolar cross terms

  2026cites this paper
• Sampling by averaging: A multiscale approach to score estimation

  2025cites this paper
• Time-space adaptive implicit-explicit method for unsteady detonations

  2025cites this paper
• Open Issues in Non-Gaussian Transport and Acceleration of Charged Energetic Particles in Space and Astrophysical Plasmas

  2025cites this paper
• Imposing quasineutrality on electrostatic plasmas via the Dirac theory of constraints

  2025cites this paper
• Friction and geometric source terms in a 1D augmented shallow water equations system

  2025cites this paper
• Numerical Approximation of the Nonlocal Ternary Viscous Cahn-Hilliard Model Based on a High Order Explicit Hybrid Algorithm

  2025cites this paper
• Peridynamic theory coupled with PHREEQC for reactive transport modeling in heterogeneous and discontinuous porous media

  2025cites this paper
• Fast simulations of X-ray absorption spectroscopy for battery materials on a quantum computer

  2025cites this paper
• A linearly implicit shock capturing scheme for compressible two-phase flows at all Mach numbers

  2025cites this paper
• Explicit Monotone Stable Super-Time-Stepping Methods for Finite Time Singularities

  2025influential citation
• Towards Numerical Method-Informed Neural Networks for PDE Learning

  2025cites this paper
• Axisymmetric gyrokinetic simulation of ASDEX-Upgrade scrape-off layer using a conservative implicit BGK collision operator

  2025cites this paper
• Semi-implicit fully exactly well-balanced schemes for the two-layer shallow water system

  2025cites this paper
• Order of Convergence of Splitting Schemes for Deterministic/Stochastic Gross-Pitaevskii Equations with Rotating Angular Momentum

  2025influential citation
• Efficient implementation of the Allen–Cahn phase-field method for material interface tracking

  2025cites this paper
• The Baker-Campbell-Hausdorff series accelerates constitutive updates

  2025cites this paper
• Splitting-based randomized dynamical low-rank approximations for stiff matrix differential equations

  2025influential citation
• Wavefunction-based simulations of 2D electronic spectroscopy of conjugated polymers: Signatures of exciton transport and coherent vibronic dynamics at finite temperature.

  2025cites this paper
• Numerical stability of force-gradient integrators and their Hessian-free variants in lattice QCD simulations

  2025cites this paper
• A Directional-ODE Framework for Discretization of Advection-Diffusion Equations

  2025cites this paper
• New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0

  2025influential citation
• An open-source solver for partially-saturated flow and multicomponent reactive transport in the hyporheic zone

  2025cites this paper
• A projection method to symmetrize the momentum flux in a vector lattice Boltzmann formulation of hydrodynamics

  2025cites this paper
• Conservation-preserved Fourier Neural Operator through Adaptive Correction

  2025cites this paper
• A GPU-based compact conservative characteristic finite volume parallel algorithm for advection diffusion equations

  2025cites this paper
• Improving the Stability and Efficiency of Operator-Splitting Methods

  2025cites this paper
• CASL-HJX: A comprehensive guide to solving deterministic and stochastic hamilton-Jacobi equations

  2025cites this paper
• A denoising multiscale particle method for nonequilibrium flow simulations

  2025cites this paper
• Petrov–Galerkin model reduction for collisional–radiative argon plasma

  2025cites this paper
• Operator Splitting Methods for Numerical Solutions of Ordinary Differential Equations

  2025cites this paper
• The role of effective mass on semiconductor charge carrier localization as revealed by the split operator method.

  2025cites this paper
• A high-order energy-conserving semi-Lagrangian discontinuous Galerkin method for the Vlasov-Ampère system

  2025cites this paper
• Deep Neural Networks for Modeling Astrophysical Nuclear Reacting Flows

  2025cites this paper
• Approximating Convective Urca Cooling in a Simmering White Dwarf

  2025cites this paper
• LRBF-Based energy-conserving time splitting schemes for the 2D Maxwell equations

  2025cites this paper
• A quantum lattice algorithm with fourth-order accuracy for the one-dimensional Dirac equation

  2025cites this paper
• An Efficient Positivity‐Preserving Finite Difference Scheme for Solving the Fokker‐Planck Diffusion Equation

  2025cites this paper
• Decoupling technology for systems of evolutionary equations

  2025cites this paper
• Operator Splitting with Compact Differences and Second-Order Two-Stage Rosenbrock Method for the Gardner Equation

  2025cites this paper
• Numerical simulation of dilute polymeric fluids with memory effects in the turbulent flow regime

  2025cites this paper
• Semi-Lagrangian methods for a plasma hybrid model with multi-species kinetic ions and massless electrons

  2025cites this paper
• Quantum magnetic J-oscillators

  2025cites this paper
• Stability and Convergence of Strang Splitting Method for the Allen-Cahn Equation with Homogeneous Neumann Boundary Condition

  2025cites this paper
• Electromagnetic field analysis of dispersive media using frequency-dependent symplectic integrator

  2025cites this paper
• An initial-boundary corrected splitting method for diffusion-reaction problems

  2025cites this paper
• Stability of the Additive Splitting Methods for the Generalized Nonlinear Schrödinger Equation

  2025cites this paper
• A comparative analysis of mesh-based and particle-based numerical methods for landslide run-out simulations

  2025cites this paper
• Heterogeneous energetic material damage simulator (HEDS): A deep learning approach to simulate damage–sensitivity linkages

  2025cites this paper
• Ordering Matters: Structure, Accuracy and Gate Cost in Second-Order Suzuki Product Formulas

  2025cites this paper
• A dynamic likelihood approach to filtering transport processes: advection-diffusion dynamics

  2025cites this paper
• Stability and convergence of multi-product expansion splitting methods with negative weights for semilinear parabolic equations

  2025cites this paper
• A novel splitting method for Vlasov-Ampere

  2025cites this paper
• Quantum simulation of elastic wave equations via Schr\"odingerisation

  2025cites this paper
• Implicit-splitting physics-driven particle relaxation for enhancement of Eulerian SPH

  2025cites this paper