Keywords: Electrohydrodynamic fluid flow; Hartmann electric number; Nonperturbative method; Convergence analysis; Strong nonlinearity; 65L10; 65L60; 34B16;
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Keywords: 65L60; 65N30; Brinkman equation; High contrast; Inf-sup condition; Preconditioning;
Keywords: Boundary layer equation; MHD flow; Rational Legendre functions; Collocation method; Hermite-Gauss points; 65L60; 41A20; 34B15;
Keywords: 65L10; 65L60; 34B16; Singular boundary value problems; Optimal quartic B-spline collocation; Convergence analysis; Error estimation; Equilibrium of the isothermal gas sphere; Thermal explosion;
Keywords: Rational Legendre; Third grade fluid; Collocation method; Porous half space; Semi-infinite interval; Chebyshev finite difference; 65L60; 41A20; 34B15; 76A05;
Keywords: Plane uncoupled thermoelasticity; Mixed boundary conditions; Boundary integral method; Cartesian harmonics; Singular behavior74B05; 74G70; 65L60
Keywords: Singularly perturbed problem; Two small parameters; Graded meshes; Galerkin finite element method65L11; 65L20; 65L60; 65L70
Keywords: 65L11; 65L20; 65L60; 65L70Singularly perturbed problem; Two small parameters; Galerkin finite element method; Bakhvalov-type mesh; Clément quasi-interpolant
Keywords: 34A36; 65P99; 65L60; 46B45; 37M99Rigorous numerics; Piecewise smooth systems; Periodic orbits; Contraction mapping theorem; Chebyshev series; Filippov
Keywords: 42C10; 35F30; 65L10; 65L60; 35K20Fourier series in special orthogonal functions; Boundary value problems for ordinary differential equation; Initial-boundary value problems for second-order parabolic equations; Boundary value problems for non-linear first
Keywords: 41A30; 65L60; 65M70; 34B40; 35L70; Generalized Hermite orthogonal approximation and interpolation; Spectral method on the whole line;
Keywords: 26A33; 65L60; 33C45; 44A45; 46C99Nonlinear fractional integro-differential equation; Collocation method; Caputo derivative; Jacobi polynomial; Operational matrix; Stability and convergence
B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems
Keywords: Derivative dependent source function; Uniform partition; Non-uniform partition; Convergence analysis; Shallow membrane cap; Thermal explosion; 65L10; 65L60; 34B16;
Nodal superconvergence of the local discontinuous Galerkin method for singularly perturbed problems
Keywords: 65L10; 65L20; 65L60; 65M50; Local discontinuous Galerkin method; Singularly perturbed problems; Local error estimates; Superconvergence;
Interpolating stabilized moving least squares (MLS) approximation for 2D elliptic interface problems
Keywords: 82B24; 65L60; Elliptic interface problems; Interpolating stabilized moving least squares approximation; Complex computational domains; Jump boundary conditions; Meshless method;
Galerkin-Levin method for highly oscillatory integrals
Keywords: 42B20; 65L60; Oscillatory integrals; Levin method; Projection methods; Galerkin methods; Ordinary differential equations;
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;
The meshless local collocation method for solving multi-dimensional Cahn-Hilliard, Swift-Hohenberg and phase field crystal equations
Keywords: Meshless methods; Local radial basis functions collocation method; Local strong form; Cahn-Hilliard equation; Swift-Hohenberg equation; Phase field crystal equation; 65M60; 65L60; 65M20;
Convergence analysis of the multistep Legendre pseudo-spectral method for Volterra integral equations with vanishing delays
Keywords: 45D05; 45G10; 41A10; 65L60; 65L70; Volterra integral equation; Multistep method; Convergence;
Efficient goal-oriented global error estimators for BDF methods using discrete adjoints
Keywords: 65L05; 65L06; 65L60; 65L20; 65L70; BDF methods; Discrete adjoints; Petrov-Galerkin discretization; Global error estimation; Dual weighted residual methodology;
Solitary-wave solutions of the GRLW equation using septic B-spline collocation method
Keywords: GRLW equation; Collocation method; Septic B-spline; Soliton; Solitary waves41A15; 65L60; 76B25
A multistep Legendre pseudo-spectral method for Volterra integral equations
Keywords: Volterra integral equation; Multistep method; Convergence; 45D05; 45G10; 41A10; 65L60; 65L70;
Smoothing transformation and spline collocation for linear fractional boundary value problems
Keywords: Fractional boundary value problem; Caputo derivative; Weakly singular integral equation; Smoothing transformation; Spline collocation method; 65L60; 65L20; 26A33;
A posteriori error analysis for finite element solution of one-dimensional elliptic differential equations using equidistributing meshes
Keywords: 65M50; 65M60; 65L50; 65L60; Mesh adaptation; Equidistribution; Error analysis; Finite element method;
Proper orthogonal decomposition variational multiscale element free Galerkin (POD-VMEFG) meshless method for solving incompressible Navier-Stokes equation
Keywords: 65L60; 65M60; 65N30; Meshless methods; Variational multiscale element free Galerkin meshless method; Proper orthogonal decomposition method; Incompressible Navier-Stokes equation;
The Sinc-collocation method for solving the Thomas–Fermi equation
Keywords: 33C45; 65L60; 34A34Thomas–Fermi equation; Sinc functions; Collocation method; Nonlinear ODE; Semi-infinite
Qualocation for a singularly perturbed boundary value problem
Keywords: 65L10; 65L12; 65L60; Reaction-convection-diffusion problems; Finite element methods; Singular perturbation; Collocation methods; Shishkin mesh; Parameter uniform convergence;
The spectral method for high order problems with proper simulations of asymptotic behaviors at infinity
Keywords: 65L60; 34B40; 41A30Laguerre quasi-orthogonal approximation; Laguerre–Gauss–Radau type interpolation; Spectral method for high order problems; Mixed inhomogeneous boundary conditions; Proper simulation of asymptotic behaviors at infinity
Convergence analysis for least-squares finite element approximations of second-order two-point boundary value problems
Keywords: 65L60; 65L70; 65L10Least-squares finite element method; Mixed method; Maximum-norm error estimate; Superconvergence; Superapproximation
A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations
Keywords: 34A30; 34L99; 65L05; 65L60; 65L70; 65G99; Constructive a posteriori estimates; Finite element method; Linear ODEs;
A numerical verification method for a periodic solution of a delay differential equation
Keywords: 65L60; 65L70Delay differential equation; Numerical computation with guaranteed accuracy; Delayed feedback control; Rössler system
On very accurate enclosure of the optimal constant in the a priori error estimates for H02-projection
Keywords: 65L10; 65L60; 65L70; 65N15; 65N30; 65N35; 65G99; 35J40Constructive a priori error estimates; Legendre polynomials; Fourth-order elliptic problem
Pseudospectral methods for solving an equation of hypergeometric type with a perturbation
Keywords: 33C45; 34L40; 65L60; 65L15; 81Q05Schrödinger operator; Regular and singular Sturm–Liouville eigenvalue problems; Pseudospectral methods; Equation of hypergeometric type; Classical orthogonal polynomials
Sinc-collocation method for solving the Blasius equation
Keywords: 34B16; 34B40; 65L60; 65M70Blasius equation; Sinc functions; Collocation method; Boundary layer equations; Exponential rate
Rational scaled generalized Laguerre function collocation method for solving the Blasius equation
Keywords: 33C45; 65L60; 34A34Blasius equation; Rational scaled generalized Laguerre function; Collocation method; Nonlinear ODE
Asymptotic and numerical stability of systems of neutral differential equations with many delays
Keywords: 65L05; 65L20; 65L60; 65M06Neutral differential equation; Asymptotic stability; Linear multistep method
A spectral Galerkin method for the coupled Orr–Sommerfeld and induction equations for free-surface MHD
Keywords: 65L15; 65L60; 76E05; 76E17; 76E25Eigenvalue problems; Spectral Galerkin method; Hydrodynamic stability; Orr–Sommerfeld equations; Free-surface MHD
Integration matrix based on arbitrary grids with a preconditioner for pseudospectral method
Keywords: 45J05; 65N35; 65L60; 41A30Pseudospectral; Preconditioner; Arbitrary grids; Random grids; Integro-differential equations
Higher order approximations using interpolation applied to collocation solutions of two-point boundary value problems
Keywords: 65D05; 41A10; 65L10; 65L60; 65L70Boundary value problems; Collocation; Hermite–Birkhoff interpolation; Asymptotic error bound
Orthogonal cubic spline collocation method for the extended Fisher-Kolmogorov equation
Keywords: 42A10; 42A15; 65L60; Extended Fisher-Kolmogorov (EFK) equation; Second-order splitting; Orthogonal cubic spline collocation method; Lyapunov functional; A priori bounds; Optimal order of convergence; Monomial basis functions; RADAU 5; Gaussian quadratur
Accurate numerical methods for the collisional motion of (heated) granular flows
Keywords: 65L60; 65R20; 76P05; 82C40; Inelastic Boltzmann equation; Spectral methods; Granular gases; Homogeneous cooling;
Metric tensors for anisotropic mesh generation
Keywords: 65M50; 65M60; 65L50; 65L60; Anisotropic mesh generation; Mesh adaptation; Equidistribution; Error analysis; Finite element method;