Keywords: 65M99; 91G20; 91G80; Radial basis functions; Repeated integrals of complementary error function; American options as free boundary problems; Artificial boundary conditions; Bernstein functions; Completely monotone functions;
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Keywords: 65H10; 65M99; 35C99; 35C07; 76B25; Nonlinear dispersive equations; Periodic traveling waves; Iterative methods for nonlinear systems; Petviashvili type methods; Fractional KdV equation; e-Boussinesq system;
Keywords: Natural gas pipeline; Glaciation; Stefan problem; Finite-element method; FreeFem++; Dirac delta function; Numerical simulation; 80A22; 80M10; 65M99;
Keywords: 35L05; 41A20; 65A05; 65M99; 65Z05; 78M25; Retarded time integral; Rational approximation; Radiation boundary conditions; Initial boundary value problem; Vlasov-Maxwell system; Accelerator beam physics;
Keywords: 65M99; 76D05; 76T99Two-phase flow; Meshfree particle method; Wetting; Contact angle
Keywords: Stochastic simulation method; Markov jump processes; Method of lines; Reaction–diffusion; Nonlinear diffusion; Radiation diffusion65C20; 68U20; 65M06; 65M20; 65M99; 60J75; 65Y9982.20.Wt; 87.10.Mn
Keywords: Reaction–diffusion system; Fast reversible reaction; Variational iteration method; Adomian’s polynomials; Auxiliary parameter35K57; 49J40; 49M27; 65M99; 65D99
Keywords: 65M08; 65M50; 65M99; 35Q86Goal-oriented a posteriori error estimate; Finite volume methods; Transport equations; Shallow water equations; Adaptive mesh refinement
Keywords: 65M99; 35B27; 92C42Homogenization; Surface reaction; Surface diffusion; Effective equations; Reaction–diffusion equations
Mimetic discretization of the Eikonal equation with Soner boundary conditions
Keywords: Eikonal equation; Mimetic gradient operators; Soner boundary conditions; Finite-differences; Quasi-Newton; Fast Marching method; 65M06; 65D25; 65M25; 65M99;
Error analysis of a meshless weak form method based on radial point interpolation technique for Sivashinsky equation arising in the alloy solidification problem
Keywords: 41A30; 65M99; 65N99; Sivashinsky equation; Meshless weak form methods; Radial point interpolation technique; Error estimate; Stability; Convergence analysis; Nonlinear biharmonic equation; Alloy solidification problem;
A meshless symplectic algorithm for nonlinear wave equation using highly accurate RBFs quasi-interpolation
Keywords: Radial basis functions; High-order quasi-interpolation; Symplectic integrator; Hamiltonian PDEs; 65M99; 65M15; 65M20; 41A05; 37K05;
An effective approach to numerical soliton solutions for the Schrödinger equation via modified cubic B-spline differential quadrature method
Keywords: Partial differential equations; Differential quadrature method; Strong stability-preserving Runge-Kutta; Modified Cubic B-splines; Schrödinger equation; 65M99; 65D07; 65L06;
Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems
Keywords: 37M25; 65M99; 65P10; 93A15; Proper orthogonal decomposition; Model reduction; Hamiltonian systems; Structure-preserving algorithms;
A new framework for solving partial differential equations using semi-analytical explicit RK(N)-type integrators
Keywords: 65M99; 35C15; 35K05; 35L03; 35L05; 65L06Semi-analytical explicit formula for PDEs; Semi-analytical explicit Runge–Kutta methods; Integral representations of solutions of PDEs; Wave equations; First-order hyperbolic equations; First-order parabolic equatio
Besov regularity of solutions to the pp-Poisson equation
Keywords: 35B35; 35J92; 41A25; 41A46; 46E35; 65M99; 65T60pp-Poisson equation; Regularity of solutions; Hölder spaces; Besov spaces; Nonlinear and adaptive approximation; Wavelets
The vlasov-poisson-boltzmann system near maxwellians for long-range interactions
Keywords: One-species Vlasov-Poisson-Boltzmann system; long-range interactions; global solutions near Maxwellians; time-velocity weighted energy method35Q20; 35Q83; 65M99; 78A35
The meshless local Petrov-Galerkin method for simulating unsteady incompressible fluid flow
Keywords: 76M25; 65M99; 65N99MLS; MLPG; Improved Gaussian’s weight; Unsteady incompressible fluid flow
Petviashvili type methods for traveling wave computations: I. Analysis of convergence
Keywords: 65H10; 65M99; 35C99; 35C07; 76B25Petviashvili type methods; Traveling wave generation; Iterative methods for nonlinear systems; Orbital convergence
RKDG methods with WENO limiters for unsteady cavitating flow
Keywords: Runge-Kutta discontinuous Galerkin method; WENO; Isentropic one-fluid model; Unsteady cavitating flow; 65M60; 65M99; 35L65;
A numerical scheme for periodic travelling-wave simulations in some nonlinear dispersive wave models
Keywords: 65M20; 65M99; 35Q53; 76B25Periodic travelling waves; Petviashvili’s method; Conserved quantities; Conservative numerical methods; Projection methods
Solving the generalized regularized long wave equation on the basis of a reproducing kernel space
Keywords: 65M99; 35C10Generalized regularized long wave equation; Reproducing kernel space
Solution of time-convolutionary Maxwell’s equations using parameter-dependent Krylov subspace reduction
Keywords: 65M99; 65M60; 86-08Dispersive medium; Convolutionary problems; Induced polarization; Fractional order PDE; Time-domain Maxwell’s system; Model reduction; Krylov subspace methods
Direct simulation of the infinitesimal dynamics of semi-discrete approximations for convection-diffusion-reaction problems
Keywords: 82.20.Wt; 87.10.Mn; 65C20; 68U20; 65M06; 65M20; 65M99; 60J75; Stochastic simulation; Markov jump processes; Diffusion; Convection; Moving cells;
Operator-splitting methods in respect of eigenvalue problems for nonlinear equations and applications for Burgers equations
Keywords: 35J60; 35J65; 65M99; 65N12; 65Z05; 74S10; 76R50Numerical analysis; Operator-splitting method; Initial value problems; Iterative solver method; Eigenvalue problem; Convection–diffusion–reaction equation
A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods
Keywords: 65R20; 65M99; 65B10; 65B15; 74B99Boundary integral method; Axisymmetric domain; Integration factor methods; Surface diffusion; Elastic stress
A high order kinetic flux-vector splitting method for the reduced five-equation model of compressible two-fluid flows
Keywords: 76T99; 65Y99; 65M99; 35L45; 35L65; 35L67Five-equation model; Kinetic flux-vector splitting schemes; Central schemes; Conservation laws; Hyperbolic systems; Shock solutions
Adaptive Runge–Kutta discontinuous Galerkin methods using different indicators: One-dimensional case
Keywords: 65M60; 65M99; 35L65Runge–Kutta discontinuous Galerkin method; Limiters; Troubled cell indicators; Adaptivity
Second order blended multidimensional upwind residual distribution scheme for steady and unsteady computations
Keywords: 65M99; 35L65; 76M10; 76M12Residual distribution scheme; Fluctuation splitting scheme; Steady problems; Unsteady problems; Finite volume method; Finite element method; Transonic flows; Shock capturing; Mass matrix; Implicit method
On a new defect of shock-capturing methods
Keywords: 76A02; 76N10; 76N15; 65M99; 65C20Shock-capturing methods; Unified coordinates; Lagrangian coordinates; Strong rarefaction waves; Contact strength
Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations
Keywords: 74S10; 76R50; 35J60; 35J65; 65M99; 65Z05; 65N12Operator-splitting methods; Explicit and implicit time discretization methods; Stability and consistency analysis; Stiff differential equations
Multi-symplectic integration of the Camassa–Holm equation
Keywords: 35Q51; 35Q53; 37K05; 37K10; 37M15; 65M06; 65M99; 65P10Camassa–Holm equation; Multi-symplecticity; Euler box scheme; Peakon–antipeakon collisions; Conservation laws
Simulation of fluid and particles flows: Asymptotic preserving schemes for bubbling and flowing regimes
Keywords: 76T10; 76T15; 76T20; 65M99; 82D05; 82C80Fluid/particle coupling; Splitting methods; Asymptotic preserving schemes; Pollutant modeling; Gravity/buoyancy dominated flows
Discontinuous fluctuation distribution
Keywords: 65M99; 76M25Fluctuation distribution; Hyperbolic conservation laws; Discontinuous representation
Time behaviour of the error when simulating finite-band periodic waves. The case of the KdV equation
Keywords: 65M20; 65M99; 35Q53; 76B25KdV; Cnoidal waves; Finite-band solutions; Conserved quantities; Conservative methods
Runge–Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
Keywords: 65M60; 65M99; 35L65Runge–Kutta discontinuous Galerkin method; Limiters; WENO finite volume scheme; High order accuracy
Modified Rayleigh conjecture method and its applications
Keywords: 35J05; 65M99; 78A40Obstacle scattering; Modified Rayleigh conjecture; Stability index method
Fast data extrapolating
Keywords: 65M99; 65D18; 68U05Data extrapolating; Huygens’ principle; Image processing on surfaces; Level set methods
Application of the parabolic spline method (PSM) to a multi-dimensional conservative semi-Lagrangian transport scheme (SLICE)
Keywords: 65M99; 76M25Advection; Cascade; Conservation; Monotonicity; PPM; Remapping
WENO schemes with Lax–Wendroff type time discretizations for Hamilton–Jacobi equations
Keywords: 65M06; 65M99; 70H20WENO scheme; Hamilton–Jacobi equation; Lax–Wendroff type time discretization; High-order accuracy
Solar cycle modelling using spatiotemporal decomposition schemes
Keywords: 85A30; 65M99; 76W05Partial differential equations; Decomposition methods; Magnetohydrodynamics; Dynamo; Solar cycle
Runge–Kutta discontinuous Galerkin methods for compressible two-medium flow simulations: One-dimensional case
Keywords: 65M60; 65M99; 35L65Runge–Kutta discontinuous Galerkin method; WENO scheme; Ghost fluid method; Approximate Riemann problem solver
Nonreflecting boundary condition for time-dependent multiple scattering
Keywords: 65M99; 74J05; 74J20; 76Q05; 78A40; 78A4543.20.FnTime-dependent waves; Wave equation; Unbounded domain; Nonreflecting boundary condition; Artificial boundary condition; Multiple scattering
An improved gas-kinetic BGK finite-volume method for three-dimensional transonic flow
Keywords: 65M99; 82C40; 76P05Navier–Stokes equations; BGK equation; Kinetic scheme; Finite-volume scheme
Numerical simulation of the fluid dynamics of 2D rigid body motion with the vortex particle method
Keywords: 65M99; 76M23; 76D25; 76Z10Numerical methods; Vortex methods; Viscous incompressible flow; Flow–structure interaction; Biological locomotion; Immersed boundary methods
A finite volume scheme for a model coupling free surface and pressurised flows in pipes
Keywords: 35L50; 35L65; 35Q35; 65M99; 76M12; 76Q05Water transients in pipes; Free-surface flows; Pressurised flows; Finite volume schemes; Roe scheme
Non-oscillatory third order fluctuation splitting schemes for steady scalar conservation laws
Keywords: 65M99; 76M25Fluctuation splitting; Hyperbolic conservation laws; Positivity; High order accuracy
Smoothed Particle ElectroMagnetics: A mesh-free solver for transients
Keywords: 65M50; 65M99; 65K05Mesh-free particle method; Smoothed particle hydrodynamics; Maxwell's equations; Electromagnetic transients
Two-dimensional compressible multimaterial flow calculations in a unified coordinate system
Keywords: 76N15; 76M25; 65M99
An adaptive local deconvolution method for implicit LES
Keywords: 65M99; 76F65; 76M25Implicit large-eddy simulation; Subgrid-scale modeling; Deconvolution; Isotropic turbulence; Taylor–Green vortex