Applied Numerical Mathematics

Article	Citations
A spectral collocation method for solving fractional KdV and KdV-Burgers equations with non-singular kernel derivatives	65
Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence	59
Numerical investigation for Caputo-Fabrizio fractional Riccati and Bernoulli equations using iterative reproducing kernel method	51
Numerical simulation of fractional evolution model arising in viscoelastic mechanics	44
Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation	43
Sharp error estimate of a compact L1-ADI scheme for the two-dimensional time-fractional integro-differential equation with singular kernels	42
Terminal value problems for the nonlinear systems of fractional differential equations	41
Numerical schemes for a class of tempered fractional integro-differential equations	40
A compact finite difference scheme for fractional Black-Scholes option pricing model	38
A POD-based reduced-order Crank-Nicolson/fourth-order alternating direction implicit (ADI) finite difference scheme for solving the two-dimensional distributed-order Riesz space-fractional diffusion e	38
An efficient Mittag-Leffler kernel approach for time-fractional advection-reaction-diffusion equation	37
A localized meshless technique for solving 2D nonlinear integro-differential equation with multi-term kernels	37
Shifted fifth-kind Chebyshev Galerkin treatment for linear hyperbolic first-order partial differential equations	37
Two spectral Legendre's derivative algorithms for Lane-Emden, Bratu equations, and singular perturbed problems	35
Transmission dynamics and sensitivity analysis of pine wilt disease with asymptomatic carriers via fractal-fractional differential operator of Mittag-Leffler kernel	34
A fourth-order least-squares based reproducing kernel method for one-dimensional elliptic interface problems	33
The formally second-order BDF ADI difference/compact difference scheme for the nonlocal evolution problem in three-dimensional space	32
Taylor wavelet solution of linear and nonlinear Lane-Emden equations	31
Orthonormal shifted discrete Legendre polynomials for solving a coupled system of nonlinear variable-order time fractional reaction-advection-diffusion equations	31
The Crank-Nicolson-type Sinc-Galerkin method for the fourth-order partial integro-differential equation with a weakly singular kernel	31
Matrix multisplitting Picard-iterative method for solving generalized absolute value matrix equation	30
A reduced-order extrapolated technique about the unknown coefficient vectors of solutions in the finite element method for hyperbolic type equation	30
Two-grid methods for semilinear time fractional reaction diffusion equations by expanded mixed finite element method	28
Fractional order Alpert multiwavelets for discretizing delay fractional differential equation of pantograph type	27
Moving least squares and spectral collocation method to approximate the solution of stochastic Volterra–Fredholm integral equations	27

Design and analysis of a numerical method for fractional neutron diffusion equation with delayed neutrons	27
Legendre wavelet method for fractional delay differential equations	27
Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem	26
A stable least residue method in reproducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel	26
Mathematical analysis and numerical methods for Caputo-Hadamard fractional diffusion-wave equations	26
A general framework for the numerical analysis of high-order finite difference solvers for nonlinear multi-term time-space fractional partial differential equations with time delay	26
A numerical method based on fractional-order generalized Taylor wavelets for solving distributed-order fractional partial differential equations	26
A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations	25
A difference scheme for the time-fractional diffusion equation on a metric star graph	25
A weak Galerkin finite element method for time fractional reaction-diffusion-convection problems with variable coefficients	24
An efficient dissipation–preserving Legendre–Galerkin spectral method for the Higgs boson equation in the de Sitter spacetime universe	23
A stable and efficient technique for linear boundary value problems by applying kernel functions	22
A reduced-order extrapolated finite difference iterative method for the Riemann-Liouville tempered fractional derivative equation	22
Convergence analysis of Crank-Nicolson extrapolated fully discrete scheme for thermally coupled incompressible magnetohydrodynamic system	22
A space-time spectral method for time-fractional Black-Scholes equation	22
A class of efficient time-stepping methods for multi-term time-fractional reaction-diffusion-wave equations	22
Parameter uniform higher order numerical treatment for singularly perturbed Robin type parabolic reaction diffusion multiple scale problems with large delay in time	22
A three-term CGPM-based algorithm without Lipschitz continuity for constrained nonlinear monotone equations with applications	21
A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers	20
Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws	20
Iterative algorithms for discrete-time periodic Sylvester matrix equations and its application in antilinear periodic system	19
Application of spectral element method for solving Sobolev equations with error estimation	19
Second-order BDF ADI Galerkin finite element method for the evolutionary equation with a nonlocal term in three-dimensional space	19
An inverse-free dynamical system for solving the absolute value equations	18
Some modified Hestenes-Stiefel conjugate gradient algorithms with application in image restoration	18
On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems	18
Analysis of versions of relaxed inertial projection and contraction method	18
A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach	18
Logarithmic Jacobi collocation method for Caputo–Hadamard fractional differential equations	17
Stability of a class of problems for time-space fractional pseudo-parabolic equation with datum measured at terminal time	17
Type (λ⁎,λ) reduced nonlocal integrable AKNS equations and their soliton solutions	17
A derivative-free RMIL conjugate gradient projection method for convex constrained nonlinear monotone equations with applications in compressive sensing	17
A second-order decoupled energy stable numerical scheme for Cahn-Hilliard-Hele-Shaw system	17
Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions	16
Superconvergent kernel functions approaches for the second kind Fredholm integral equations	16
Exponential Jacobi-Galerkin method and its applications to multidimensional problems in unbounded domains	16
A Galerkin meshless reproducing kernel particle method for numerical solution of neutral delay time-space distributed-order fractional damped diffusion-wave equation	16
An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noise	16
Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix	16
A meshless method for time fractional nonlinear mixed diffusion and diffusion-wave equation	16
A new approximation of conformable time fractional partial differential equations with proportional delay	15
Large-scale regression with non-convex loss and penalty	15
On the identification of nonlinear terms in the generalized Camassa-Holm equation involving dual-power law nonlinearities	15
A unified spectral collocation method for nonlinear systems of multi-dimensional integral equations with convergence analysis	15
Fractional-order Boubaker wavelets method for solving fractional Riccati differential equations	15
Iterated fractional Tikhonov regularization method for solving the spherically symmetric backward time-fractional diffusion equation	15
Optimal point-wise error estimate of two conservative fourth-order compact finite difference schemes for the nonlinear Dirac equation	15
A new representation of generalized averaged Gauss quadrature rules	14
A high-order numerical scheme for solving nonlinear time fractional reaction-diffusion equations with initial singularity	14
Error analysis of an implicit Galerkin meshfree scheme for general second-order parabolic problems	14

A second-order unconditionally stable method for the anisotropic dendritic crystal growth model with an orientation-field	14
Numerical investigations of shallow water waves via generalized equal width (GEW) equation	14
Positivity preserving stochastic θ-methods for selected SDEs	14
A semi-analytical approach to Caputo type time-fractional modified anomalous sub-diffusion equations	13
Fourier spectral approximation for time fractional Burgers equation with nonsmooth solutions	13
Tensor Krylov subspace methods with an invertible linear transform product applied to image processing	13
Effective condition number for the selection of the RBF shape parameter with the fictitious point method	13
A doubly relaxed minimal-norm Gauss–Newton method for underdetermined nonlinear least-squares problems	13
Filon quadrature for stochastic oscillators driven by time-varying forces	13
Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations	13
A new three-level fourth-order compact finite difference scheme for the extended Fisher-Kolmogorov equation	13
A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations	13
An optimal control approach for determining the source term in fractional diffusion equation by different cost functionals	13
Superconvergence error estimate of Galerkin method for Sobolev equation with Burgers' type nonlinearity	13
A high-order accurate finite difference scheme for the KdV equation with time-periodic boundary forcing	13
Effect of an efficient numerical integration technique on the element-free Galerkin method	13
Energy-preserving exponential integrator Fourier pseudo-spectral schemes for the nonlinear Dirac equation	13
Global convergence of a descent PRP type conjugate gradient method for nonconvex optimization	13
Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense	12
A preconditioned fast finite element approximation to variable-order time-fractional diffusion equations in multiple space dimensions	12
A splitting method for SDEs with locally Lipschitz drift: Illustration on the FitzHugh-Nagumo model	12
A preconditioner based on sine transform for two-dimensional semi-linear Riesz space fractional diffusion equations in convex domains	12
The performance of a numerical scheme on the variable-order time-fractional advection-reaction-subdiffusion equations	12
Strong-order conditions of Runge-Kutta method for stochastic optimal control problems	12
Convergence results of two-step inertial proximal point algorithm	12
A new approach for solving one-dimensional fractional boundary value problems via Haar wavelet collocation method	12
Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law	12
Stable numerical schemes for time-fractional diffusion equation with generalized memory kernel	12
On the Hermitian and skew-Hermitian splitting-like iteration approach for solving complex continuous-time algebraic Riccati matrix equation	12
Pointwise error analysis of the BDF3 compact finite difference scheme for viscous Burgers' equations	12
Rotational pressure-correction method for the Stokes/Darcy model based on the modular grad-div stabilization	12
Vieta-Lucas polynomials for the coupled nonlinear variable-order fractional Ginzburg-Landau equations	12
A third-order accurate in time method for boundary layer flow problems	12
A second order fractional step hybrid numerical algorithm for time delayed singularly perturbed 2D convection-diffusion problems	11
A meshless finite difference method for elliptic interface problems based on pivoted QR decomposition	11
Tensor Krylov subspace methods via the Einstein product with applications to image and video processing	11
A numerical scheme for a class of generalized Burgers' equation based on Haar wavelet nonstandard finite difference method	11
Approximation methods with inertial term for large-scale nonlinear monotone equations	11
A stabilized fully-discrete scheme for phase field crystal equation	11
A numerical method for the solution of nonlinear Volterra Hammerstein integral equations of the third-kind	11
An energy-preserving and efficient scheme for a double-fractional conservative Klein–Gordon–Zakharov system	11
A divergence-free generalized moving least squares approximation with its application	11
A multi-domain spectral collocation method for Volterra integral equations with a weakly singular kernel	11
A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with energy-preservation for long-time dynamics of the nonlinear Klein-Gordon equation	11
Linearly implicit variable step-size BDF schemes with Fourier pseudospectral approximation for incompressible Navier-Stokes equations	11
Two moments consistent discrete formulation for binary breakage population balance equation and its convergence	11
On the improvement of the triangular Shepard method by non conformal polynomial elements	11
Iterative approximation of fixed points and applications to two-point second-order boundary value problems and to machine learning	11
A fast numerical method for fractional partial integro-differential equations with spatial-time delays	11
A unified enrichment approach of the standard three-node triangular element	11
Novel linear decoupled and unconditionally energy stable numerical methods for the modified phase field crystal model	11
Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels	11
α-Robust H1-norm convergence analysis of ADI scheme for two-dimensional time-fractional diffusion equation	11
A partially proximal S-ADMM for separable convex optimization with linear constraints	11
Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments	11
An hp-version of the discontinuous Galerkin time-stepping method for Volterra integral equations with weakly singular kernels	10
A reduced-order extrapolated model based on splitting implicit finite difference scheme and proper orthogonal decomposition for the fourth-order nonlinear Rosenau equation	10
An asymptotic preserving semi-implicit multiderivative solver	10
Efficient energy preserving Galerkin–Legendre spectral methods for fractional nonlinear Schrödinger equation with wave operator	10
Defect-deferred correction method based on a subgrid artificial viscosity model for fluid-fluid interaction	10
Monotone iterative technique for solving finite difference systems of time fractional parabolic equations with initial/periodic conditions	10
An explicit stable finite difference method for the Allen–Cahn equation	10
A new analysis of Galerkin Legendre spectral methods for coupled hyperbolic/parabolic system arising in unsteady MHD flow of Maxwell fluid and numerical simulation	10
Energy stable numerical schemes for the fractional-in-space Cahn–Hilliard equation	10
A moving grid finite element method applied to a mechanobiochemical model for 3D cell migration	10
A two-grid block-centered finite difference method for the nonlinear regularized long wave equation	10
A numerical method for linear Volterra integral equations on infinite intervals and its application to the resolution of metastatic tumor growth models	10
The lowest-order stabilizer free weak Galerkin finite element method	10
Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using Generalized Finite Difference Method	10
A fourth-order conservative difference scheme for the Riesz space-fractional Sine-Gordon equations and its fast implementation	10
Modified weak Galerkin method with weakly imposed boundary condition for convection-dominated diffusion equations	10
An efficient second order stabilized scheme for the two dimensional time fractional Allen-Cahn equation	10
Convergence analysis of a second-order semi-implicit projection method for Landau-Lifshitz equation	10
A numerical scheme with divergence free H-div triangular finite element for the Stokes equations	10
Uniform error bounds of exponential wave integrator methods for the long-time dynamics of the Dirac equation with small potentials	10
A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization	10
Implicit and semi-implicit well-balanced finite-volume methods for systems of balance laws	10
Temporal error analysis of Euler semi-implicit scheme for the magnetohydrodynamics equations with variable density	9
Uniformly convergent NIPG method for singularly perturbed convection diffusion problem on Shishkin type meshes	9
The stability study of numerical solution of Fredholm integral equations of the first kind with emphasis on its application in boundary elements method	9

Supercloseness of finite element method on a Bakhvalov-type mesh for a singularly perturbed problem with two parameters	9
A linear, high-order, and unconditionally energy stable scheme for the epitaxial thin film growth model without slope selection	9
A new conservative fourth-order accurate difference scheme for the nonlinear Schrödinger equation with wave operator	9
Decoupled modified characteristic finite element method with different subdomain time steps for nonstationary dual–porosity–Navier–Stokes model	9
A splitting uniformly convergent method for one-dimensional parabolic singularly perturbed convection-diffusion systems	9
On the convergence analysis and stability of the RBF-adaptive method for the forward-backward heat problem in 2D	9
The discrete maximum principle and energy stability of a new second-order difference scheme for Allen-Cahn equations	9
Numerical scheme for solving a porous Saint-Venant type model for water flow on vegetated hillslopes	9
Galerkin finite element method for damped nonlinear Schrödinger equation	9
Two-dimensional Gegenbauer wavelets for the numerical solution of tempered fractional model of the nonlinear Klein-Gordon equation	9
An hp-version Chebyshev collocation method for nonlinear fractional differential equations	9
Foundations of space-time finite element methods: Polytopes, interpolation, and integration	9
A weak divergence CDG method for the biharmonic equation on triangular and tetrahedral meshes	9
Affine-invariant WENO weights and operator	9
Double parameter splitting (DPS) iteration method for solving complex symmetric linear systems	9
On convergence rates of Kaczmarz-type methods with different selection rules of working rows	9
Penalty method for indifference pricing of American option in a liquidity switching market	9
Analysis and numerical solution of the generalized proportional fractional Cauchy problem	9
Strong convergence and stability of the split-step theta method for highly nonlinear neutral stochastic delay integro differential equation	9
Solving tensor absolute value equation	9
Communication in complex networks	9
Analytical and numerical solutions of time-fractional advection-diffusion-reaction equation	9
High-order Runge-Kutta discontinuous Galerkin methods with multi-resolution WENO limiters for solving steady-state problems	9
Numerical approximations of a hydro-dynamically coupled phase-field model for binary mixture of passive/active nematic liquid crystals and viscous fluids	9
A fast difference scheme for the variable coefficient time-fractional diffusion wave equations	8
A parallel stabilized finite element variational multiscale method based on fully overlapping domain decomposition for the incompressible Navier-Stokes equations	8
A highly accurate and computationally efficient technique for solving the electrohydrodynamic flow in a circular cylindrical conduit	8
Numerical analysis of a dual-phase-lag model with microtemperatures	8
A wavelet collocation method based on Gegenbauer scaling function for solving fourth-order time-fractional integro-differential equations with a weakly singular kernel	8
Perturbation analysis for total least squares problems with linear equality constraint	8
Numerical analysis of linearly implicit Euler-Riemann method for nonlinear Gurtin-MacCamy model	8
On numerical solution of Fredholm and Hammerstein integral equations via Nyström method and Gaussian quadrature rules for splines	8
Issues with positivity-preserving Patankar-type schemes	8
An all Froude high order IMEX scheme for the shallow water equations on unstructured Voronoi meshes	8
Arbitrarily high order structure-preserving algorithms for the Allen-Cahn model with a nonlocal constraint	8
Analysis of the linearly energy- and mass-preserving finite difference methods for the coupled Schrödinger-Boussinesq equations	8
Adaptive Hermite spectral methods in unbounded domains	8
Identifying an unknown source term in a time-space fractional parabolic equation	8
An efficient energy-preserving method for the two-dimensional fractional Schrödinger equation	8
Fast parallel-in-time quasi-boundary value methods for backward heat conduction problems	8
A modified optimization method for robust partial quadratic eigenvalue assignment using receptances and system matrices	8
An effective alternating direction method of multipliers for color image restoration	8
Fractional Romanovski–Jacobi tau method for time-fractional partial differential equations with nonsmooth solutions	8
Temporal high-order, unconditionally maximum-principle-preserving integrating factor multi-step methods for Allen-Cahn-type parabolic equations	8
An advancement approach of Haar wavelet method and Bratu-type equations	8
Efficient numerical methods for the nonlinear two-sided space-fractional diffusion equation with variable coefficients	8
The stabilized penalty-projection finite element method for the Navier-Stokes-Cahn-Hilliard-Oono system	8
Positivity and boundedness preserving numerical scheme for the stochastic epidemic model with square-root diffusion term	8
An analysis on the penalty and Nitsche's methods for the Stokes–Darcy system with a curved interface	8
A guide to the finite and virtual element methods for elasticity	8
A Crank-Nicolson-type compact difference method with the uniform time step for a class of weakly singular parabolic integro-differential equations	8
The power method and beyond	8
A geometric probability randomized Kaczmarz method for large scale linear systems	8
Splitting schemes for non-stationary problems with a rational approximation for fractional powers of the operator	8
An explicit algorithm for solving monotone variational inequalities	8
Error analysis and approximation of Jacobi pseudospectral method for the integer and fractional order integro-differential equation	8
On the filtered polynomial interpolation at Chebyshev nodes	7
Comparison of two finite element schemes for a chemo-repulsion system with quadratic production	7
A class of spectral three-term descent Hestenes-Stiefel conjugate gradient algorithms for large-scale unconstrained optimization and image restoration problems	7
Iterative compact finite difference method for the numerical study of fully wet porous fins with different profile shapes	7
An augmented memoryless BFGS method based on a modified secant equation with application to compressed sensing	7
New primal-dual weak Galerkin finite element methods for convection-diffusion problems	7
Explicit methods based on barycentric rational interpolants for solving non-stiff Volterra integral equations	7
Numerical treatment of a singularly perturbed 2-D convection-diffusion elliptic problem with Robin-type boundary conditions	7
A parameter-uniform numerical method for singularly perturbed Robin type parabolic convection-diffusion turning point problems	7
A third-order WENO scheme based on exponential polynomials for Hamilton-Jacobi equations	7
An implicit semi-linear discretization of a bi-fractional Klein–Gordon–Zakharov system which conserves the total energy	7
Combined real and imaginary parts method for solving generalized Lyapunov matrix equation	7
A novel modified TRSVD method for large-scale linear discrete ill-posed problems	7
An extrapolated CN-WSGD OSC method for a nonlinear time fractional reaction-diffusion equation	7
Solving a non-linear fractional convection-diffusion equation using local discontinuous Galerkin method	7
Some iterative approaches for Sylvester tensor equations, Part I: A tensor format of truncated Loose Simpler GMRES	7
Unconditional superconvergence of the fully-discrete schemes for nonlinear prey-predator model	7
A second-order numerical approximation of a singularly perturbed nonlinear Fredholm integro-differential equation	7
An adaptive iterative linearised finite element method for implicitly constituted incompressible fluid flow problems and its application to Bingham fluids	7
Energy-preserving finite element methods for a class of nonlinear wave equations	7
A Crank-Nicolson ADI quadratic spline collocation method for two-dimensional Riemann-Liouville space-fractional diffusion equations	7
Spectral approximation methods for non equilibrium transport in turbulent channel flows using fADE	7
A comprehensive theory on generalized BBKS schemes	7
Numerical solution of nonlinear advection diffusion reaction equation using high-order compact difference method	7
Square-root filtering via covariance SVD factors in the accurate continuous-discrete extended-cubature Kalman filter	7
LDG approximation of a nonlinear fractional convection-diffusion equation using B-spline basis functions	7
Convergence and numerical simulations of prey-predator interactions via a meshless method	7
Efficient two-step Runge-Kutta methods for fluid dynamics simulations	7
Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients	7
Fast difference scheme for the reaction-diffusion-advection equation with exact artificial boundary conditions	7
A multi-parameter parallel ADMM for multi-block linearly constrained separable convex optimization	7
The energy-preserving time high-order AVF compact finite difference scheme for nonlinear wave equations in two dimensions	7
Unconditionally optimal convergence of a linearized Galerkin FEM for the nonlinear time-fractional mobile/immobile transport equation	7
A posteriori error estimates for weak Galerkin methods for second order elliptic problems on polygonal meshes	7
Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space distributed-order diffusion equation	7
A novel two-step streamline-diffusion FEM for singularly perturbed 2D parabolic PDEs	7
A randomized exponential canonical correlation analysis method for data analysis and dimensionality reduction	7
High-order conservative schemes for the space fractional nonlinear Schrödinger equation	7
Double reduction order method based conservative compact schemes for the Rosenau equation	7