Keywords: 65Q20; 65M06; Difference scheme; Partial delay differential equation; Retardation; Time delay;
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Keywords: 35R11; 65M06; 65M12Fractional differential equation; Caputo derivative; Diffusion equation; Implicit finite difference method; Distributed order equation
Keywords: 65M06; 92-08; 92C99Time dependent partial differential equations; Finite difference methods; Velocity-based moving meshes; Mass conservation
Keywords: 35L70; 65M06; 65M12; Nonlinear hyperbolic equation; Energy stability; Positivity; Linear iteration; Convergence analysis;
Keywords: 35R11; 65M06; 65N30Multi-term time fractional diffusion-wave equations; High order compact finite difference; Galerkin spectral method; Solvability; Energy method; Convergence and stability
Keywords: 65M06; 65M12Wave equation in polar co-ordinates; Non-polynomial tension spline; Maximum absolute errors
Keywords: 65M60; 65M12; 65M06; 35S10; 65R20; Finite element methods; Fractional differential equations; Convergence analysis;
Keywords: 65M06; 65M22; 65M25; 76D05Computational fluid dynamics; Lattice Boltzmann method; Unbounded domain; Non-reflecting boundary conditions; Characteristic boundary conditions; LODI
Keywords: 65M06; 65M12; 35B10; 35Q53Shallow water waves of moderate amplitude; Conservative solutions; Wave breaking
Keywords: 92B05; 92D25; 92D40; 65M06; Computational model; Mathematical ecology; Microbial film; Nonlinear modeling; Finite-difference method;
Keywords: 35K45; 35K90; 47D60; 65M06; 65M55Numerical analysis; Operator-splitting method; Initial value problems; Iterative solver method; Nonlinear equations
Keywords: Cahn–Hilliard equation; Nonuniform grid; Finite difference method; Multigrid method65M55; 65M06
Keywords: 26A33; 65M06; 65M12; 65M55; 65T50High-order finite difference method; Fractional substantial derivative; Weighted average operator; Stability analysis; Nonsmooth solution
Keywords: micropolar fluid flow; initial-boundary value problem; free boundary; finite difference approximations; strong and weak convergence35Q35; 76M20; 65M06; 76N99
Stability and convergence of characteristic MAC scheme and post-processing for the Oseen equations on non-uniform grids
Keywords: Characteristic MAC scheme; Stability; Oseen equations; Post-processing; Non-uniform grids; 65M06; 65M12; 65M15; 65M25; 76D07;
A high-order L2-compact difference method for Caputo-type time-fractional sub-diffusion equations with variable coefficients
Keywords: Fractional sub-diffusion equation; Variable coefficient; Compact difference method; High-order convergence; Energy method; 65M06; 65M12; 65M15; 35R11;
The solution of nonlinear Green-Naghdi equation arising in water sciences via a meshless method which combines moving kriging interpolation shape functions with the weighted essentially non-oscillatory method
Keywords: Moving kriging interpolation; Weighted essentially non-oscillatory (WENO) method; Green-Naghdi equation; Water science; 65M06; 65M60;
Analysis and numerical simulation of multicomponent system with Atangana-Baleanu fractional derivative
Keywords: Mittag-Leffler; Fractional derivative; Hopf-bifurcation; Oscillations; Predator-prey; Stability analysis; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Robustness of fractional difference schemes via the Caputo subdiffusion-reaction equations
Keywords: Caputo derivative; Difference methods; Fractional subdiffusion-reaction systems; Pattern formation; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
The 6th-order weighted ENO schemes for hyperbolic conservation laws
Keywords: WENO scheme; Spurious oscillation; Hyperbolic conservation laws; 65M06; 65M20;
High-order numerical approximation formulas for Riemann-Liouville (Riesz) tempered fractional derivatives: construction and application (I)
Keywords: Normalized Riesz tempered derivative; (2,2) Padé approximation; Normalized Riemann-Liouville tempered derivative; 65A05; 65D15; 65D25; 65M06; 65M12;
Smooth Quintic spline approximation for nonlinear Schrödinger equations with variable coefficients in one and two dimensions
Keywords: Quintic polynomial spline; Schrödinger equation; Variable coefficients; Convergence; Stability; Mass and energy conservations; 65M06; 65M12; 65M15;
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;
Efficient and accurate numerical simulation of acoustic wave propagation in a 2D heterogeneous media
Keywords: Acoustic wave equation; Compact finite difference method; Padé approximation; Alternative direction implicit; Heterogenous media; 65M06; 65M32; 65N06;
Difference methods for parabolic equations with Robin condition
Keywords: Parabolic differential functional equation; Implicit difference method; Recurrent equation; Estimate of solution; Convergence; Stability; 35R10; 35B30; 65M12; 65M06;
An efficient and conservative compact finite difference scheme for the coupled Gross-Pitaevskii equations describing spin-1 Bose-Einstein condensate
Keywords: Coupled Gross-Pitaevskii equations; Compact finite difference method; Linearized and decoupled scheme; Conservation laws; Lifting technique; Optimal error estimate; 65M06; 65M12;
3D mathematical model and numerical simulation for laying marine cable along prescribed trajectory on seabed
Keywords: Partial differential equation; Free boundary; Numerical simulation; Marine cable; Cable laying; 35Q35; 35R35; 35L53; 35L70; 65M06;
Stability and error estimates of a new high-order compact ADI method for the unsteady 3D convection-diffusion equation
Keywords: Convection-diffusion equation; Finite difference method; ADI method; Stability analysis; Error estimate; 65M06; 65M12; 65M15;
Inverse multi-quadric RBF for computing the weights of FD method: Application to American options
Keywords: Radial basis function; RBF-FD method; FD weights; American option; Inverse multi-quadric; 65M70; 91B25; 65M06;
The new mass-conserving S-DDM scheme for two-dimensional parabolic equations with variable coefficients
Keywords: Parabolic equations; Variable coefficients; Mass-conserving; Block-divided domain decomposition; Stability; Error estimate; 65N06; 65N12; 65M06; 65Y05; 76R05;
Conditional full stability of positivity-preserving finite difference scheme for diffusion-advection-reaction models
Keywords: 65M06; 65M12; 65M20; Diffusion-advection-reaction; Semi-discretization; Exponential time differencing; Finite difference; Numerical analysis;
A new adaptive weighted essentially non-oscillatory WENO-θ scheme for hyperbolic conservation laws
Keywords: 76N15; 35L65; 35L67; 65M06; Hyperbolic conservation laws; Euler equations; Shock-capturing methods; Weighted essentially non-oscillatory (WENO) schemes; Adaptive upwind-central schemes; Smoothness indicators;
A least squares augmented immersed interface method for solving Navier-Stokes and Darcy coupling equations
Keywords: Navier-Stokes and Darcy coupling; Coupled fluid flow with porous media; Least squares augmented IIM; Fast Poisson/Helmholtz solver; Analytic solution for Navier-Stokes and Darcy coupling; Interface relations; 65M06; 65M85; 76M20;
Global BV solution for a non-local coupled system modeling the dynamics of dislocation densities
Keywords: 35Q53; 35Q72; 49L25; 35F25; 35L40; 35L45; 65M06; 65M12; 65M15; 74H20; 74H25; Hamilton-Jacobi system; Non-local eikonal system; Non-local transport system; BV estimate; Discontinuous viscosity solution; Dislocation dynamics;
Analysis and application of new fractional Adams-Bashforth scheme with Caputo-Fabrizio derivative
Keywords: Caputo-Fabrizio derivative; Fractional Adams-Bashforth method; Error analysis; Nonlinear chaotic systems; Numerical simulations; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
A class of two-level implicit unconditionally stable methods for a fourth order parabolic equation
Keywords: Fourth-order parabolic equations; Two-level implicit method; Three spatial grid points; Unconditionally stable; Tri-diagonal system; Maximum absolute errors; 65M06; 65M22;
A modification on strictly positive definite RBF-DQ method based on matrix decomposition
Keywords: 65M20; 65M06; Radial basis functions; Strictly positive definite functions; Positive definite matrix; Matrix decomposition;
Numerical approximation of nonlinear fractional parabolic differential equations with Caputo-Fabrizio derivative in Riemann-Liouville sense
Keywords: Caputo-Fabrizio derivative; Exponential decay-law; Exponential time differencing; Finite difference method; Fractional nonlinear PDEs; Numerical simulations; Riemann-Liouville definition; 34A34; 35A05; 35K57; 65L05; 65M06; 93C10;
Nonstandard finite difference method for solving the multi-strain TB model
Keywords: Nonstandard finite difference method; Epidemic model; Tuberculosis M/XDR-TB; Convergence analysis and stability of numerical methods; 37N25; 35A24; 65M06;
Analysis of a new finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation
Keywords: Fractional diffusion-wave equation; Time fractional derivative; Local discontinuous Galerkin method; Stability; 65M12; 65M06; 35S10;
RBF-FD method for the high dimensional time fractional convection-diffusion equation
Keywords: 35R11; 65M06; 65M12; Time fractional convection-diffusion equation; RBF-FD method; Wendland RBF; Shifted Grünwald formula; Stability and convergence;
High-order finite difference technique for delay pseudo-parabolic equations
Keywords: 65M06; 65M12; 65M15; 65M22; Pseudo-parabolic equation; Delay difference scheme; Error estimate;
Fast numerical valuation of options with jump under Merton's model
Keywords: 65M06; 65M55; 65L60; 91B25; 91G60; 65J10; European option pricing; American option pricing; Merton's jump-diffusion model; Finite difference methods; Discontinuous Galerkin finite element methods; Multigrid methods;
A second order Crank-Nicolson scheme for fractional Cattaneo equation based on new fractional derivative
Keywords: Second order; New fractional derivative; Crank-Nicolson; Cattaneo equation; Finite difference; 65M06; 65M12; 65M15; 26A33;
A modified Bhattacharya exponential method to approximate positive and bounded solutions of the Burgers-Fisher equation
Keywords: 65M06; 65M22; 65Q10; Burgers-Fisher equation; Exponential method; Modified Bhattacharya approach; Non-negativity; Boundedness; Monotonicity;
Multi-conformal-symplectic PDEs and discretizations
Keywords: 65M06; 37L50; Multi-symplectic PDE; Structure-preserving algorithm; Conformal symplectic;
The weighted ENO scheme based on the modified smoothness indicator
Keywords: WENO scheme; Smoothness indicator; Hyperbolic conservation laws; 65M06; 65M20;
A matched Peaceman-Rachford ADI method for solving parabolic interface problems
Keywords: Heat equation; Parabolic interface problem; Matched alternating direction implicit (ADI) method; Peaceman-Rachford ADI scheme; Matched interface and boundary (MIB); 65M06; 65M12; 35K05;
Block-centered finite difference methods for general Darcy-Forchheimer problems
Keywords: Block-centered finite difference; General Darcy-Forchheimer problems; Numerical analysis; Second-order accuracy; 65M06; 65M12; 65M15;
High-order ADI scheme for option pricing in stochastic volatility models
Keywords: 65M06; 91B28; Option pricing; Stochastic volatility models; Mixed derivatives; High-order ADI scheme;