Applied Numerical Mathematics

Article	Citations
Numerical simulation of initial value problems with generalized Caputo-type fractional derivatives	119
Collocation methods for terminal value problems of tempered fractional differential equations	68
A high accuracy numerical method and its convergence for time-fractional Black-Scholes equation governing European options	67
A spectral collocation method for solving fractional KdV and KdV-Burgers equations with non-singular kernel derivatives	61
An accurate spectral collocation method for nonlinear systems of fractional differential equations and related integral equations with nonsmooth solutions	58
Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence	56
The PRP conjugate gradient algorithm with a modified WWP line search and its application in the image restoration problems	50
Global consistency analysis of L1-Galerkin spectral schemes for coupled nonlinear space-time fractional Schrödinger equations	49
Numerical investigation for Caputo-Fabrizio fractional Riccati and Bernoulli equations using iterative reproducing kernel method	45
Numerical simulation of fractional evolution model arising in viscoelastic mechanics	40
An alternating direction implicit orthogonal spline collocation method for the two dimensional multi-term time fractional integro-differential equation	39
A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation	39
Terminal value problems for the nonlinear systems of fractional differential equations	37
Investigation of the Oldroyd model as a generalized incompressible Navier–Stokes equation via the interpolating stabilized element free Galerkin technique	36
Numerical solutions of hybrid fuzzy differential equations in a Hilbert space	36
Sharp error estimate of a compact L1-ADI scheme for the two-dimensional time-fractional integro-differential equation with singular kernels	36
Numerical solution of nonlinear 2D optimal control problems generated by Atangana-Riemann-Liouville fractal-fractional derivative	35
Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation	34
An efficient Mittag-Leffler kernel approach for time-fractional advection-reaction-diffusion equation	33
Bricks for the mixed high-order virtual element method: Projectors and differential operators	32
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	32
Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations	32
Numerical schemes for a class of tempered fractional integro-differential equations	32
Shifted fifth-kind Chebyshev Galerkin treatment for linear hyperbolic first-order partial differential equations	31
A conjugate gradient algorithm and its applications in image restoration	31

A localized meshless technique for solving 2D nonlinear integro-differential equation with multi-term kernels	31
A fourth-order least-squares based reproducing kernel method for one-dimensional elliptic interface problems	31
Two spectral Legendre's derivative algorithms for Lane-Emden, Bratu equations, and singular perturbed problems	30
A compact finite difference scheme for fractional Black-Scholes option pricing model	30
A note on the optimal degree of the weak gradient of the stabilizer free weak Galerkin finite element method	29
Numerical methods for the nonlocal wave equation of the peridynamics	28
The formally second-order BDF ADI difference/compact difference scheme for the nonlocal evolution problem in three-dimensional space	28
A novel algorithm based on the Legendre wavelets spectral technique for solving the Lane–Emden equations	28
Conjugate-symplecticity properties of Euler–Maclaurin methods and their implementation on the Infinity Computer	28
A local discontinuous Galerkin method for time-fractional diffusion equation with discontinuous coefficient	27
Two-grid methods for semilinear time fractional reaction diffusion equations by expanded mixed finite element method	26
The Crank-Nicolson-type Sinc-Galerkin method for the fourth-order partial integro-differential equation with a weakly singular kernel	26
Parameter-uniform numerical treatment of singularly perturbed initial-boundary value problems with large delay	26
Orthonormal shifted discrete Legendre polynomials for solving a coupled system of nonlinear variable-order time fractional reaction-advection-diffusion equations	25
A fourth-order non-uniform mesh optimal B-spline collocation method for solving a strongly nonlinear singular boundary value problem describing electrohydrodynamic flow of a fluid	25
Arbitrary high-order, conservative and positivity preserving Patankar-type deferred correction schemes	25
A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation	24
Matrix multisplitting Picard-iterative method for solving generalized absolute value matrix equation	24
Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem	24
Two fast and efficient linear semi-implicit approaches with unconditional energy stability for nonlocal phase field crystal equation	24
A stable least residue method in reproducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel	24
Transmission dynamics and sensitivity analysis of pine wilt disease with asymptomatic carriers via fractal-fractional differential operator of Mittag-Leffler kernel	24
Long-term analysis of stochastic θ-methods for damped stochastic oscillators	24
Design and analysis of a numerical method for fractional neutron diffusion equation with delayed neutrons	24
A Tau–like numerical method for solving fractional delay integro–differential equations	23
A reduced-order extrapolated technique about the unknown coefficient vectors of solutions in the finite element method for hyperbolic type equation	23
A difference scheme for the time-fractional diffusion equation on a metric star graph	23
An efficient dissipation–preserving Legendre–Galerkin spectral method for the Higgs boson equation in the de Sitter spacetime universe	23
Iterative Tikhonov regularization of tensor equations based on the Arnoldi process and some of its generalizations	22
Moving least squares and spectral collocation method to approximate the solution of stochastic Volterra–Fredholm integral equations	22
Implicit-explicit time integration of nonlinear fractional differential equations	21
Taylor wavelet solution of linear and nonlinear Lane-Emden equations	21
Solution of Benjamin-Bona-Mahony-Burgers equation using collocation method with quintic Hermite splines	21
A class of efficient time-stepping methods for multi-term time-fractional reaction-diffusion-wave equations	21
A stable and efficient technique for linear boundary value problems by applying kernel functions	21
Conservative limiting method for high-order bicompact schemes as applied to systems of hyperbolic equations	21
A weak Galerkin finite element method for time fractional reaction-diffusion-convection problems with variable coefficients	21
A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations	21
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	21
The local discontinuous Galerkin finite element methods for Caputo-type partial differential equations: Mathematical analysis	21
Mathematical analysis and numerical methods for Caputo-Hadamard fractional diffusion-wave equations	21
A reduced-order extrapolated finite difference iterative method for the Riemann-Liouville tempered fractional derivative equation	20
Legendre wavelet collocation method combined with the Gauss–Jacobi quadrature for solving fractional delay-type integro-differential equations	20
A numerical method based on fractional-order generalized Taylor wavelets for solving distributed-order fractional partial differential equations	20
Explicit, ninth order, two step methods for solving inhomogeneous linear problems x″(t)=Λx(t)+f(t)	20
Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation	20
Fractional order Alpert multiwavelets for discretizing delay fractional differential equation of pantograph type	19
Space-time finite element method for the distributed-order time fractional reaction diffusion equations	19
Convergence analysis of Crank-Nicolson extrapolated fully discrete scheme for thermally coupled incompressible magnetohydrodynamic system	19
Legendre wavelet method for fractional delay differential equations	19

The energy-preserving finite difference methods and their analyses for system of nonlinear wave equations in two dimensions	19
Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation	19
Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws	18
Vector rational and semi-rational rogue waves for the coupled cubic-quintic nonlinear Schrödinger system in a non-Kerr medium	18
Solving system of second-order BVPs using a new algorithm based on reproducing kernel Hilbert space	18
Application of spectral element method for solving Sobolev equations with error estimation	17
A novel iterative method for the solution of a nonlinear matrix equation	17
On accurate solution of the Fredholm integral equations of the second kind	17
Time two-grid algorithm based on finite difference method for two-dimensional nonlinear fractional evolution equations	17
Superconvergent kernel functions approaches for the second kind Fredholm integral equations	16
A meshless method for time fractional nonlinear mixed diffusion and diffusion-wave equation	16
Structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrödinger equation	16
On the hexagonal Shepard method	16
A new SOR-like method for solving absolute value equations	16
A space-time spectral method for time-fractional Black-Scholes equation	16
A three-term CGPM-based algorithm without Lipschitz continuity for constrained nonlinear monotone equations with applications	16
The time discontinuous space-time finite element method for fractional diffusion-wave equation	15
Numerical solutions of space-fractional advection-diffusion equations with nonlinear source term	15
Exponential Jacobi-Galerkin method and its applications to multidimensional problems in unbounded domains	15
A new multiscale algorithm for solving second order boundary value problems	15
Analysis of versions of relaxed inertial projection and contraction method	15
Numerical study for two types variable-order Burgers' equations with proportional delay	15
A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach	15
Iterative algorithms for discrete-time periodic Sylvester matrix equations and its application in antilinear periodic system	15
Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix	15
On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems	15
Optimal point-wise error estimate of two conservative fourth-order compact finite difference schemes for the nonlinear Dirac equation	15
A second-order decoupled energy stable numerical scheme for Cahn-Hilliard-Hele-Shaw system	15
A derivative-free RMIL conjugate gradient projection method for convex constrained nonlinear monotone equations with applications in compressive sensing	15
A meshless technique based on generalized moving least squares combined with the second-order semi-implicit backward differential formula for numerically solving time-dependent phase field models on t	15
Convergence and superconvergence analysis of finite element methods for the time fractional diffusion equation	15
Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations	15
Error analysis of an implicit Galerkin meshfree scheme for general second-order parabolic problems	14
An efficient numerical technique for variable order time fractional nonlinear Klein-Gordon equation	14
Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions	14
A HJB-POD approach for the control of nonlinear PDEs on a tree structure	14
High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on triangular meshes	14
A unified spectral collocation method for nonlinear systems of multi-dimensional integral equations with convergence analysis	14
Stability of a class of problems for time-space fractional pseudo-parabolic equation with datum measured at terminal time	14
On the identification of nonlinear terms in the generalized Camassa-Holm equation involving dual-power law nonlinearities	14
A new approximation of conformable time fractional partial differential equations with proportional delay	14
A Galerkin meshless reproducing kernel particle method for numerical solution of neutral delay time-space distributed-order fractional damped diffusion-wave equation	14
Fractional-order Boubaker wavelets method for solving fractional Riccati differential equations	14
An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noise	14
Some three-term conjugate gradient methods with the new direction structure	13
Large-scale regression with non-convex loss and penalty	13
Some modified Hestenes-Stiefel conjugate gradient algorithms with application in image restoration	13
Numerical investigations of shallow water waves via generalized equal width (GEW) equation	13
Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points	13
A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers	13
Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximation	13
A low cost and highly accurate technique for big data spatial-temporal interpolation	13
Iterated fractional Tikhonov regularization method for solving the spherically symmetric backward time-fractional diffusion equation	13
GeCo: Geometric Conservative nonstandard schemes for biochemical systems	13
A preconditioned fast finite element approximation to variable-order time-fractional diffusion equations in multiple space dimensions	12
A new approach for solving one-dimensional fractional boundary value problems via Haar wavelet collocation method	12
A weak Galerkin finite element method for solving time-fractional coupled Burgers' equations in two dimensions	12
A third-order accurate in time method for boundary layer flow problems	12
On the implementation of a finite volumes scheme with monotone transmission conditions for scalar conservation laws on a star-shaped network	12
Tamed Runge-Kutta methods for SDEs with super-linearly growing drift and diffusion coefficients	12
Soft computing technique for a system of fuzzy Volterra integro-differential equations in a Hilbert space	12
Fast compact implicit integration factor method with non-uniform meshes for the two-dimensional nonlinear Riesz space-fractional reaction-diffusion equation	12
Some high order formulae for approximating Caputo fractional derivatives	12
Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme	12
Superconvergence error estimate of Galerkin method for Sobolev equation with Burgers' type nonlinearity	12
Energy-preserving exponential integrator Fourier pseudo-spectral schemes for the nonlinear Dirac equation	12
Solution of multi-dimensional Fredholm equations using Legendre scaling functions	12
Logarithmic Jacobi collocation method for Caputo–Hadamard fractional differential equations	12
Superconvergence of the gradient approximation for weak Galerkin finite element methods on nonuniform rectangular partitions	12
A meshless finite difference method for elliptic interface problems based on pivoted QR decomposition	11
A high-order accurate finite difference scheme for the KdV equation with time-periodic boundary forcing	11
Operator splitting schemes for American options under the two-asset Merton jump-diffusion model	11
Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations	11
Strong-order conditions of Runge-Kutta method for stochastic optimal control problems	11
A computational method for a class of systems of nonlinear variable-order fractional quadratic integral equations	11
A multi-step scheme based on cubic spline for solving backward stochastic differential equations	11
Fourier spectral approximation for time fractional Burgers equation with nonsmooth solutions	11
An inverse-free dynamical system for solving the absolute value equations	11
Filon quadrature for stochastic oscillators driven by time-varying forces	11
A doubly relaxed minimal-norm Gauss–Newton method for underdetermined nonlinear least-squares problems	11

Positivity preserving stochastic θ-methods for selected SDEs	11
A new representation of generalized averaged Gauss quadrature rules	11
A divergence-free generalized moving least squares approximation with its application	11
A high-order numerical scheme for solving nonlinear time fractional reaction-diffusion equations with initial singularity	11
The performance of a numerical scheme on the variable-order time-fractional advection-reaction-subdiffusion equations	11
Extended block boundary value methods for neutral equations with piecewise constant argument	11
A virtual element method for the Laplacian eigenvalue problem in mixed form	11
Stable numerical schemes for time-fractional diffusion equation with generalized memory kernel	10
Iterative approximation of fixed points and applications to two-point second-order boundary value problems and to machine learning	10
A generalized collocation method in reproducing kernel space for solving a weakly singular Fredholm integro-differential equations	10
A semi-analytical approach to Caputo type time-fractional modified anomalous sub-diffusion equations	10
Pointwise error analysis of the BDF3 compact finite difference scheme for viscous Burgers' equations	10
A fast numerical method for fractional partial integro-differential equations with spatial-time delays	10
A second-order unconditionally stable method for the anisotropic dendritic crystal growth model with an orientation-field	10
A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations	10
Effective new methods for automated parameter selection in regularized inverse problems	10
Numerical solution of linear fractional weakly singular integro-differential equations with integral boundary conditions	10
Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels	10
Vieta-Lucas polynomials for the coupled nonlinear variable-order fractional Ginzburg-Landau equations	10
An energy-preserving and efficient scheme for a double-fractional conservative Klein–Gordon–Zakharov system	10
A class of globally convergent three-term Dai-Liao conjugate gradient methods	10
An optimal control approach for determining the source term in fractional diffusion equation by different cost functionals	10
Numerical analysis for the Cahn-Hilliard-Hele-Shaw system with variable mobility and logarithmic Flory-Huggins potential	10
Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation	10
The lowest-order stabilizer free weak Galerkin finite element method	10
A preconditioner based on sine transform for two-dimensional semi-linear Riesz space fractional diffusion equations in convex domains	9
A reduced-order extrapolated model based on splitting implicit finite difference scheme and proper orthogonal decomposition for the fourth-order nonlinear Rosenau equation	9
A compact ADI scheme for two-dimensional fractional sub-diffusion equation with Neumann boundary condition	9
A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with energy-preservation for long-time dynamics of the nonlinear Klein-Gordon equation	9
Tensor Krylov subspace methods with an invertible linear transform product applied to image processing	9
Defect-deferred correction method based on a subgrid artificial viscosity model for fluid-fluid interaction	9
Two moments consistent discrete formulation for binary breakage population balance equation and its convergence	9
Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments	9
A linear, high-order, and unconditionally energy stable scheme for the epitaxial thin film growth model without slope selection	9
Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law	9
Efficient and energy stable method for the Cahn-Hilliard phase-field model for diblock copolymers	9
Convergence analysis of a second-order semi-implicit projection method for Landau-Lifshitz equation	9
On the Hermitian and skew-Hermitian splitting-like iteration approach for solving complex continuous-time algebraic Riccati matrix equation	9
A new three-level fourth-order compact finite difference scheme for the extended Fisher-Kolmogorov equation	9
Nonlinear stability and convergence of ERKN integrators for solving nonlinear multi-frequency highly oscillatory second-order ODEs with applications to semi-linear wave equations	9
Global convergence of a descent PRP type conjugate gradient method for nonconvex optimization	9
A fourth-order conservative difference scheme for the Riesz space-fractional Sine-Gordon equations and its fast implementation	9
A second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equation	9
A second order fractional step hybrid numerical algorithm for time delayed singularly perturbed 2D convection-diffusion problems	9
A multi-domain spectral collocation method for Volterra integral equations with a weakly singular kernel	9
Novel linear decoupled and unconditionally energy stable numerical methods for the modified phase field crystal model	9
Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense	9
Analysis and numerical solution of the generalized proportional fractional Cauchy problem	9
An hp-version Chebyshev collocation method for nonlinear fractional differential equations	9
A partially proximal S-ADMM for separable convex optimization with linear constraints	9
Energy preserving relaxation method for space-fractional nonlinear Schrödinger equation	9
An efficient second order stabilized scheme for the two dimensional time fractional Allen-Cahn equation	8
Existence of solutions of an explicit energy-conserving scheme for a fractional Klein–Gordon–Zakharov system	8
Transformed implicit-explicit second derivative diagonally implicit multistage integration methods with strong stability preserving explicit part	8
Numerical approximation of the dynamic Koiter's model for the hyperbolic parabolic shell	8
Perturbation analysis for total least squares problems with linear equality constraint	8
A second-order accurate scheme for two-dimensional space fractional diffusion equations with time Caputo-Fabrizio fractional derivative	8
A numerical scheme for a class of generalized Burgers' equation based on Haar wavelet nonstandard finite difference method	8
Error analysis of a time-splitting method for incompressible flows with variable density	8
Efficient solution of large-scale algebraic Riccati equations associated with index-2 DAEs via the inexact low-rank Newton-ADI method	8
Strong stability preserving second derivative diagonally implicit multistage integration methods	8
A parallel stabilized finite element variational multiscale method based on fully overlapping domain decomposition for the incompressible Navier-Stokes equations	8
A new analysis of Galerkin Legendre spectral methods for coupled hyperbolic/parabolic system arising in unsteady MHD flow of Maxwell fluid and numerical simulation	8
Strong convergence and stability of the split-step theta method for highly nonlinear neutral stochastic delay integro differential equation	8
Analysis of the linearly energy- and mass-preserving finite difference methods for the coupled Schrödinger-Boussinesq equations	8
Multilinear PageRank: Uniqueness, error bound and perturbation analysis	8
Efficient iterative solvers for a complex valued two-by-two block linear system with application to parabolic optimal control problems	8
An asymptotic preserving semi-implicit multiderivative solver	8
Numerical scheme for solving a porous Saint-Venant type model for water flow on vegetated hillslopes	8
A stable meshfree PDE solver for source-type flows in porous media	8
Linearly implicit variable step-size BDF schemes with Fourier pseudospectral approximation for incompressible Navier-Stokes equations	8
Uniform error bounds of exponential wave integrator methods for the long-time dynamics of the Dirac equation with small potentials	8
Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using Generalized Finite Difference Method	8
Modified weak Galerkin method with weakly imposed boundary condition for convection-dominated diffusion equations	8
Energy stable numerical schemes for the fractional-in-space Cahn–Hilliard equation	8
Numerical solutions of system of two-dimensional Volterra integral equations via Legendre wavelets and convergence	8
A stable finite element method for low inertia undulatory locomotion in three dimensions	8
Solution of differential algebraic equations with the Fredholm operator by the least squares method	8
Effect of an efficient numerical integration technique on the element-free Galerkin method	8
A dissipative finite difference Fourier pseudo-spectral method for the symmetric regularized long wave equation with damping mechanism	8
On the convergence analysis and stability of the RBF-adaptive method for the forward-backward heat problem in 2D	8
Well-balanced central schemes for the one and two-dimensional Euler systems with gravity	8
Galerkin finite element method for damped nonlinear Schrödinger equation	8
A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization	8
Novel fractional time-stepping algorithms for natural convection problems with variable density	8
Communication in complex networks	8
A splitting method for SDEs with locally Lipschitz drift: Illustration on the FitzHugh-Nagumo model	8
Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients	7
Smoothing transformation for numerical solution of nonlinear weakly singular Volterra integral equations using quasilinearization and product integration methods	7
An hp-version of the discontinuous Galerkin time-stepping method for Volterra integral equations with weakly singular kernels	7
A positivity-preserving finite volume scheme for three-temperature radiation diffusion equations	7
The stabilized penalty-projection finite element method for the Navier-Stokes-Cahn-Hilliard-Oono system	7
Efficient numerical methods for the nonlinear two-sided space-fractional diffusion equation with variable coefficients	7
Foundations of space-time finite element methods: Polytopes, interpolation, and integration	7
Solving tensor absolute value equation	7