Applied Numerical Mathematics

Papers
(The TQCC of Applied Numerical Mathematics is 7. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2020-05-01 to 2024-05-01.)
ArticleCitations
Numerical simulation of initial value problems with generalized Caputo-type fractional derivatives123
A high accuracy numerical method and its convergence for time-fractional Black-Scholes equation governing European options71
Collocation methods for terminal value problems of tempered fractional differential equations70
A spectral collocation method for solving fractional KdV and KdV-Burgers equations with non-singular kernel derivatives62
An accurate spectral collocation method for nonlinear systems of fractional differential equations and related integral equations with nonsmooth solutions58
Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence57
The PRP conjugate gradient algorithm with a modified WWP line search and its application in the image restoration problems51
Global consistency analysis of L1-Galerkin spectral schemes for coupled nonlinear space-time fractional Schrödinger equations49
Numerical investigation for Caputo-Fabrizio fractional Riccati and Bernoulli equations using iterative reproducing kernel method47
Numerical simulation of fractional evolution model arising in viscoelastic mechanics41
An alternating direction implicit orthogonal spline collocation method for the two dimensional multi-term time fractional integro-differential equation41
Sharp error estimate of a compact L1-ADI scheme for the two-dimensional time-fractional integro-differential equation with singular kernels40
A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation39
Numerical solutions of hybrid fuzzy differential equations in a Hilbert space38
Terminal value problems for the nonlinear systems of fractional differential equations38
Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation37
Numerical schemes for a class of tempered fractional integro-differential equations35
Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations34
An efficient Mittag-Leffler kernel approach for time-fractional advection-reaction-diffusion equation33
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 e33
Bricks for the mixed high-order virtual element method: Projectors and differential operators32
A localized meshless technique for solving 2D nonlinear integro-differential equation with multi-term kernels32
A fourth-order least-squares based reproducing kernel method for one-dimensional elliptic interface problems32
Two spectral Legendre's derivative algorithms for Lane-Emden, Bratu equations, and singular perturbed problems31
A compact finite difference scheme for fractional Black-Scholes option pricing model31
Shifted fifth-kind Chebyshev Galerkin treatment for linear hyperbolic first-order partial differential equations31
Numerical methods for the nonlocal wave equation of the peridynamics31
A conjugate gradient algorithm and its applications in image restoration30
The formally second-order BDF ADI difference/compact difference scheme for the nonlocal evolution problem in three-dimensional space29
Parameter-uniform numerical treatment of singularly perturbed initial-boundary value problems with large delay29
Conjugate-symplecticity properties of Euler–Maclaurin methods and their implementation on the Infinity Computer28
A novel algorithm based on the Legendre wavelets spectral technique for solving the Lane–Emden equations28
A local discontinuous Galerkin method for time-fractional diffusion equation with discontinuous coefficient27
The Crank-Nicolson-type Sinc-Galerkin method for the fourth-order partial integro-differential equation with a weakly singular kernel27
Transmission dynamics and sensitivity analysis of pine wilt disease with asymptomatic carriers via fractal-fractional differential operator of Mittag-Leffler kernel27
Arbitrary high-order, conservative and positivity preserving Patankar-type deferred correction schemes26
Orthonormal shifted discrete Legendre polynomials for solving a coupled system of nonlinear variable-order time fractional reaction-advection-diffusion equations26
Two-grid methods for semilinear time fractional reaction diffusion equations by expanded mixed finite element method26
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 fluid26
Matrix multisplitting Picard-iterative method for solving generalized absolute value matrix equation26
A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation25
A reduced-order extrapolated technique about the unknown coefficient vectors of solutions in the finite element method for hyperbolic type equation25
A stable least residue method in reproducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel25
Moving least squares and spectral collocation method to approximate the solution of stochastic Volterra–Fredholm integral equations25
Design and analysis of a numerical method for fractional neutron diffusion equation with delayed neutrons25
Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem25
A Tau–like numerical method for solving fractional delay integro–differential equations24
Conservative limiting method for high-order bicompact schemes as applied to systems of hyperbolic equations24
Solution of Benjamin-Bona-Mahony-Burgers equation using collocation method with quintic Hermite splines24
A numerical method for two-dimensional multi-term time-space fractional nonlinear diffusion-wave equations23
Fractional order Alpert multiwavelets for discretizing delay fractional differential equation of pantograph type23
A numerical method based on fractional-order generalized Taylor wavelets for solving distributed-order fractional partial differential equations23
An efficient dissipation–preserving Legendre–Galerkin spectral method for the Higgs boson equation in the de Sitter spacetime universe23
A difference scheme for the time-fractional diffusion equation on a metric star graph23
A weak Galerkin finite element method for time fractional reaction-diffusion-convection problems with variable coefficients23
Arbitrarily high-order energy-preserving schemes for the Camassa-Holm equation22
Taylor wavelet solution of linear and nonlinear Lane-Emden equations22
A class of efficient time-stepping methods for multi-term time-fractional reaction-diffusion-wave equations22
Legendre wavelet method for fractional delay differential equations22
Iterative Tikhonov regularization of tensor equations based on the Arnoldi process and some of its generalizations22
Mathematical analysis and numerical methods for Caputo-Hadamard fractional diffusion-wave equations22
A stable and efficient technique for linear boundary value problems by applying kernel functions21
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 delay21
Implicit-explicit time integration of nonlinear fractional differential equations21
Interior penalty discontinuous Galerkin technique for solving generalized Sobolev equation21
The energy-preserving finite difference methods and their analyses for system of nonlinear wave equations in two dimensions20
Explicit, ninth order, two step methods for solving inhomogeneous linear problems x″(t)=Λx(t)+f(t)20
Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws20
Convergence analysis of Crank-Nicolson extrapolated fully discrete scheme for thermally coupled incompressible magnetohydrodynamic system20
A reduced-order extrapolated finite difference iterative method for the Riemann-Liouville tempered fractional derivative equation20
Solving system of second-order BVPs using a new algorithm based on reproducing kernel Hilbert space20
Space-time finite element method for the distributed-order time fractional reaction diffusion equations19
Time two-grid algorithm based on finite difference method for two-dimensional nonlinear fractional evolution equations19
Vector rational and semi-rational rogue waves for the coupled cubic-quintic nonlinear Schrödinger system in a non-Kerr medium18
A three-term CGPM-based algorithm without Lipschitz continuity for constrained nonlinear monotone equations with applications18
A space-time spectral method for time-fractional Black-Scholes equation18
A novel iterative method for the solution of a nonlinear matrix equation18
Application of spectral element method for solving Sobolev equations with error estimation18
A new SOR-like method for solving absolute value equations18
Structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrödinger equation17
Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations17
Numerical study for two types variable-order Burgers' equations with proportional delay16
Superconvergent kernel functions approaches for the second kind Fredholm integral equations16
On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems16
Stability of a class of problems for time-space fractional pseudo-parabolic equation with datum measured at terminal time16
A meshless method for time fractional nonlinear mixed diffusion and diffusion-wave equation16
A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach16
A new approximation of conformable time fractional partial differential equations with proportional delay15
A unified spectral collocation method for nonlinear systems of multi-dimensional integral equations with convergence analysis15
An analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noise15
Optimal point-wise error estimate of two conservative fourth-order compact finite difference schemes for the nonlinear Dirac equation15
Exponential Jacobi-Galerkin method and its applications to multidimensional problems in unbounded domains15
Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix15
Convergence and superconvergence analysis of finite element methods for the time fractional diffusion equation15
A Galerkin meshless reproducing kernel particle method for numerical solution of neutral delay time-space distributed-order fractional damped diffusion-wave equation15
Fractional-order Boubaker wavelets method for solving fractional Riccati differential equations15
A second-order decoupled energy stable numerical scheme for Cahn-Hilliard-Hele-Shaw system15
A HJB-POD approach for the control of nonlinear PDEs on a tree structure15
A derivative-free RMIL conjugate gradient projection method for convex constrained nonlinear monotone equations with applications in compressive sensing15
On the identification of nonlinear terms in the generalized Camassa-Holm equation involving dual-power law nonlinearities15
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 t15
Analysis of versions of relaxed inertial projection and contraction method15
An inverse-free dynamical system for solving the absolute value equations15
Error estimates in weak Galerkin finite element methods for parabolic equations under low regularity assumptions15
Numerical solutions of space-fractional advection-diffusion equations with nonlinear source term15
Iterative algorithms for discrete-time periodic Sylvester matrix equations and its application in antilinear periodic system15
A new multiscale algorithm for solving second order boundary value problems15
Error analysis of an implicit Galerkin meshfree scheme for general second-order parabolic problems14
An efficient numerical technique for variable order time fractional nonlinear Klein-Gordon equation14
Some modified Hestenes-Stiefel conjugate gradient algorithms with application in image restoration14
Logarithmic Jacobi collocation method for Caputo–Hadamard fractional differential equations14
Large-scale regression with non-convex loss and penalty14
High-order Runge-Kutta discontinuous Galerkin methods with a new type of multi-resolution WENO limiters on triangular meshes14
A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers14
Soft computing technique for a system of fuzzy Volterra integro-differential equations in a Hilbert space13
A low cost and highly accurate technique for big data spatial-temporal interpolation13
Tamed Runge-Kutta methods for SDEs with super-linearly growing drift and diffusion coefficients13
GeCo: Geometric Conservative nonstandard schemes for biochemical systems13
A high-order numerical scheme for solving nonlinear time fractional reaction-diffusion equations with initial singularity13
Iterated fractional Tikhonov regularization method for solving the spherically symmetric backward time-fractional diffusion equation13
Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximation13
Numerical investigations of shallow water waves via generalized equal width (GEW) equation13
Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points13
Fast compact implicit integration factor method with non-uniform meshes for the two-dimensional nonlinear Riesz space-fractional reaction-diffusion equation12
A new representation of generalized averaged Gauss quadrature rules12
Some high order formulae for approximating Caputo fractional derivatives12
A preconditioned fast finite element approximation to variable-order time-fractional diffusion equations in multiple space dimensions12
A full-discrete exponential Euler approximation of the invariant measure for parabolic stochastic partial differential equations12
A weak Galerkin finite element method for solving time-fractional coupled Burgers' equations in two dimensions12
On the implementation of a finite volumes scheme with monotone transmission conditions for scalar conservation laws on a star-shaped network12
Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme12
Energy-preserving exponential integrator Fourier pseudo-spectral schemes for the nonlinear Dirac equation12
A new approach for solving one-dimensional fractional boundary value problems via Haar wavelet collocation method12
Fourier spectral approximation for time fractional Burgers equation with nonsmooth solutions12
A high-order accurate finite difference scheme for the KdV equation with time-periodic boundary forcing12
A third-order accurate in time method for boundary layer flow problems12
Superconvergence error estimate of Galerkin method for Sobolev equation with Burgers' type nonlinearity12
A doubly relaxed minimal-norm Gauss–Newton method for underdetermined nonlinear least-squares problems12
An optimal control approach for determining the source term in fractional diffusion equation by different cost functionals11
A new three-level fourth-order compact finite difference scheme for the extended Fisher-Kolmogorov equation11
Two moments consistent discrete formulation for binary breakage population balance equation and its convergence11
Iterative approximation of fixed points and applications to two-point second-order boundary value problems and to machine learning11
Vieta-Lucas polynomials for the coupled nonlinear variable-order fractional Ginzburg-Landau equations11
A generalized collocation method in reproducing kernel space for solving a weakly singular Fredholm integro-differential equations11
Optimal rotated block-diagonal preconditioning for discretized optimal control problems constrained with fractional time-dependent diffusive equations11
The performance of a numerical scheme on the variable-order time-fractional advection-reaction-subdiffusion equations11
Filon quadrature for stochastic oscillators driven by time-varying forces11
Numerical solution of the Cauchy problem for Volterra integrodifferential equations with difference kernels11
Second-order BDF ADI Galerkin finite element method for the evolutionary equation with a nonlocal term in three-dimensional space11
A virtual element method for the Laplacian eigenvalue problem in mixed form11
A meshless finite difference method for elliptic interface problems based on pivoted QR decomposition11
A fast numerical method for fractional partial integro-differential equations with spatial-time delays11
Operator splitting schemes for American options under the two-asset Merton jump-diffusion model11
Effect of an efficient numerical integration technique on the element-free Galerkin method11
A semi-analytical approach to Caputo type time-fractional modified anomalous sub-diffusion equations11
Pointwise error analysis of the BDF3 compact finite difference scheme for viscous Burgers' equations11
A computational method for a class of systems of nonlinear variable-order fractional quadratic integral equations11
Positivity preserving stochastic θ-methods for selected SDEs11
A divergence-free generalized moving least squares approximation with its application11
A second order fractional step hybrid numerical algorithm for time delayed singularly perturbed 2D convection-diffusion problems11
Stable numerical schemes for time-fractional diffusion equation with generalized memory kernel11
Strong-order conditions of Runge-Kutta method for stochastic optimal control problems11
Solving fractal-fractional differential equations using operational matrix of derivatives via Hilfer fractal-fractional derivative sense10
The lowest-order stabilizer free weak Galerkin finite element method10
A second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equation10
An energy-preserving and efficient scheme for a double-fractional conservative Klein–Gordon–Zakharov system10
A second-order accurate scheme for two-dimensional space fractional diffusion equations with time Caputo-Fabrizio fractional derivative10
A second-order unconditionally stable method for the anisotropic dendritic crystal growth model with an orientation-field10
A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with energy-preservation for long-time dynamics of the nonlinear Klein-Gordon equation10
α-Robust H1-norm convergence analysis of ADI scheme for two-dimensional time-fractional diffusion equation10
A splitting method for SDEs with locally Lipschitz drift: Illustration on the FitzHugh-Nagumo model10
A class of globally convergent three-term Dai-Liao conjugate gradient methods10
Least-squares ReLU neural network (LSNN) method for scalar nonlinear hyperbolic conservation law10
Effective new methods for automated parameter selection in regularized inverse problems10
On the Hermitian and skew-Hermitian splitting-like iteration approach for solving complex continuous-time algebraic Riccati matrix equation10
Defect-deferred correction method based on a subgrid artificial viscosity model for fluid-fluid interaction10
A partially proximal S-ADMM for separable convex optimization with linear constraints10
Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments10
Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation10
A fourth-order conservative difference scheme for the Riesz space-fractional Sine-Gordon equations and its fast implementation10
Well-balanced central schemes for the one and two-dimensional Euler systems with gravity10
A numerical scheme for a class of generalized Burgers' equation based on Haar wavelet nonstandard finite difference method9
Novel linear decoupled and unconditionally energy stable numerical methods for the modified phase field crystal model9
Nonlinear stability and convergence of ERKN integrators for solving nonlinear multi-frequency highly oscillatory second-order ODEs with applications to semi-linear wave equations9
Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using Generalized Finite Difference Method9
Modified weak Galerkin method with weakly imposed boundary condition for convection-dominated diffusion equations9
Energy preserving relaxation method for space-fractional nonlinear Schrödinger equation9
A reduced-order extrapolated model based on splitting implicit finite difference scheme and proper orthogonal decomposition for the fourth-order nonlinear Rosenau equation9
Effective condition number for the selection of the RBF shape parameter with the fictitious point method9
Convergence analysis of a second-order semi-implicit projection method for Landau-Lifshitz equation9
Efficient energy preserving Galerkin–Legendre spectral methods for fractional nonlinear Schrödinger equation with wave operator9
Uniform error bounds of exponential wave integrator methods for the long-time dynamics of the Dirac equation with small potentials9
Tensor Krylov subspace methods with an invertible linear transform product applied to image processing9
Rotational pressure-correction method for the Stokes/Darcy model based on the modular grad-div stabilization9
Global convergence of a descent PRP type conjugate gradient method for nonconvex optimization9
A multi-domain spectral collocation method for Volterra integral equations with a weakly singular kernel9
A compact ADI scheme for two-dimensional fractional sub-diffusion equation with Neumann boundary condition9
A numerical scheme with divergence free H-div triangular finite element for the Stokes equations9
Numerical scheme for solving a porous Saint-Venant type model for water flow on vegetated hillslopes9
Convergence results of two-step inertial proximal point algorithm9
Analysis and numerical solution of the generalized proportional fractional Cauchy problem9
An hp-version Chebyshev collocation method for nonlinear fractional differential equations9
A linear, high-order, and unconditionally energy stable scheme for the epitaxial thin film growth model without slope selection9
Efficient and energy stable method for the Cahn-Hilliard phase-field model for diblock copolymers9
A preconditioner based on sine transform for two-dimensional semi-linear Riesz space fractional diffusion equations in convex domains9
Multilinear PageRank: Uniqueness, error bound and perturbation analysis9
Transformed implicit-explicit second derivative diagonally implicit multistage integration methods with strong stability preserving explicit part8
Fractional Romanovski–Jacobi tau method for time-fractional partial differential equations with nonsmooth solutions8
Novel fractional time-stepping algorithms for natural convection problems with variable density8
A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization8
Error analysis and approximation of Jacobi pseudospectral method for the integer and fractional order integro-differential equation8
The stabilized penalty-projection finite element method for the Navier-Stokes-Cahn-Hilliard-Oono system8
Existence of solutions of an explicit energy-conserving scheme for a fractional Klein–Gordon–Zakharov system8
A moving grid finite element method applied to a mechanobiochemical model for 3D cell migration8
A new analysis of Galerkin Legendre spectral methods for coupled hyperbolic/parabolic system arising in unsteady MHD flow of Maxwell fluid and numerical simulation8
An efficient second order stabilized scheme for the two dimensional time fractional Allen-Cahn equation8
The discrete maximum principle and energy stability of a new second-order difference scheme for Allen-Cahn equations8
Perturbation analysis for total least squares problems with linear equality constraint8
A dissipative finite difference Fourier pseudo-spectral method for the symmetric regularized long wave equation with damping mechanism8
Linearly implicit variable step-size BDF schemes with Fourier pseudospectral approximation for incompressible Navier-Stokes equations8
Efficient solution of large-scale algebraic Riccati equations associated with index-2 DAEs via the inexact low-rank Newton-ADI method8
Efficient numerical methods for the nonlinear two-sided space-fractional diffusion equation with variable coefficients8
An explicit algorithm for solving monotone variational inequalities8
Communication in complex networks8
Numerical solutions of system of two-dimensional Volterra integral equations via Legendre wavelets and convergence8
Determination of regularization parameter via solving a multi-objective optimization problem8
Strong convergence and stability of the split-step theta method for highly nonlinear neutral stochastic delay integro differential equation8
An hp-version of the discontinuous Galerkin time-stepping method for Volterra integral equations with weakly singular kernels8
A weak divergence CDG method for the biharmonic equation on triangular and tetrahedral meshes8
An asymptotic preserving semi-implicit multiderivative solver8
On the convergence analysis and stability of the RBF-adaptive method for the forward-backward heat problem in 2D8
Penalty method for indifference pricing of American option in a liquidity switching market8
Galerkin finite element method for damped nonlinear Schrödinger equation8
Uniformly convergent NIPG method for singularly perturbed convection diffusion problem on Shishkin type meshes8
A stabilized fully-discrete scheme for phase field crystal equation8
Smoothing transformation for numerical solution of nonlinear weakly singular Volterra integral equations using quasilinearization and product integration methods8
A parallel stabilized finite element variational multiscale method based on fully overlapping domain decomposition for the incompressible Navier-Stokes equations8
Decoupled modified characteristic finite element method with different subdomain time steps for nonstationary dual–porosity–Navier–Stokes model8
Analysis of the linearly energy- and mass-preserving finite difference methods for the coupled Schrödinger-Boussinesq equations8
Energy stable numerical schemes for the fractional-in-space Cahn–Hilliard equation8
A stable finite element method for low inertia undulatory locomotion in three dimensions8
Efficient iterative solvers for a complex valued two-by-two block linear system with application to parabolic optimal control problems8
A numerical method for the solution of nonlinear Volterra Hammerstein integral equations of the third-kind7
A fast difference scheme for the variable coefficient time-fractional diffusion wave equations7
An explicit stable finite difference method for the Allen–Cahn equation7
Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients7
Solving tensor absolute value equation7
A new conservative fourth-order accurate difference scheme for the nonlinear Schrödinger equation with wave operator7
Foundations of space-time finite element methods: Polytopes, interpolation, and integration7
A positivity-preserving finite volume scheme for three-temperature radiation diffusion equations7
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