Numerical Algorithms

Article	Citations
Unconditionally convergent and superconvergent finite element method for nonlinear time-fractional parabolic equations with distributed delay	52
A real unconstrained equivalent problem of the quaternion equality constrained weighted least squares problem	35
Uniform convergence of optimal order for a finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation with parabolic layers	31
A modified generalized version of projected reflected gradient method in Hilbert spaces	26
An edgewise iterative scheme for the discontinuous Galerkin method with Lagrange multiplier for Poisson’s equation	26
A posteriori error estimates for the time-dependent convection-diffusion-reaction equation coupled with the Darcy system	24
A bidiagonalization-based numerical algorithm for computing the inverses of (p,q)-tridiagonal matrices	23
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	22
A fast and high-order IMEX method for non-linear time-space-fractional reaction-diffusion equations	21
Efficient second-order, linear, decoupled and unconditionally energy stable schemes of the Cahn-Hilliard-Darcy equations for the Hele-Shaw flow	21
Finding global minima with an inflection point-based filled function algorithm	21
Stability improvements for fast matrix multiplication	19
Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing	18
On estimating the separation associated with the periodic continuous Sylvester equation	18
Oscillation-preserving Legendre-Galerkin methods for second kind integral equations with highly oscillatory kernels	16
Fractional Tikhonov regularization and error estimation in inverse source problems for Biharmonic equations: a priori and a posteriori analysis under deterministic and random perturbations	15
A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem	15
A Modified Iteration Method for an Inverse Problem of Diffusion Equation with Laplace and Riesz-Feller Space Fractional Operators	15
Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition	15
Convergence of the Nelder-Mead method	14
Operational Jacobi Galerkin method for a class of cordial Volterra integral equations	14
Local and parallel partition of unity scheme for the mixed Navier-Stokes-Darcy problem	14
Some combined techniques of spectral conjugate gradient methods with applications to robotic and image restoration models	14
A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes	13
A feasible proximal bundle algorithm with convexification for nonsmooth, nonconvex semi-infinite programming	13

Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair	12
The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids	12
A posteriori error bounds for the block-Lanczos method for matrix function approximation	12
Solution of the Cauchy problem for the Brinkman equations using an alternating method of fundamental solutions	11
Two-grid finite element method for the dual-permeability-Stokes fluid flow model	11
The application of Goeken–Johnson’s Runge–Kutta methods in unconstrained convex optimization	11
An Uzawa-DOS method for solving saddle-point problems	11
Preconditioned golden ratio primal-dual algorithm with linesearch	11
Spectral characterizations and integer powers of tridiagonal 2-Toeplitz matrices	11
Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model	11
On the rational approximation of Markov functions, with applications to the computation of Markov functions of Toeplitz matrices	11
A novel meshless approach based on new fractional spaces for solving nonlinear Riesz space distributed order reaction-diffusion equations with non-smooth solutions and stability analysis	11
A note on the Grcar matrix	11
A strong sequential optimality condition for cardinality-constrained optimization problems	11
A sign-based linear method for horizontal linear complementarity problems	11
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	10
A novel higher-order efficient computational method for pricing European and Asian options	10
Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method	10
Convergence analysis of the augmented Lagrangian method for $$\ell _{p}$$-norm cone optimization problems with $$p \ge 2$$	10
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions	10
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime	10
Computation of incomplete beta function ratios $$I_{x}(a,b)$$ with Deuflhard’s algorithm	10
A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds	9
A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations	9
Fast algorithms for interpolation and smoothing for a general class of fourth order exponential splines	9
On the randomized multiple row-action methods for solving linear least-squares problems	9
An Ulm-like algorithm for generalized inverse eigenvalue problems	9
A multi-physical structure-preserving method and its analysis for the conservative Allen-Cahn equation with nonlocal constraint	9
Tensor randomized extended Kaczmarz methods for large inconsistent tensor linear equations with t-product	9
A priori error estimates of a discontinuous Galerkin method for the Navier-Stokes equations	9
Modified globally convergent Polak-Ribière-Polyak conjugate gradient methods with self-correcting property for large-scale unconstrained optimization	9
Fractal interpolation on the real projective plane	9
Improved uniform error bounds of Lawson-type exponential integrator method for long-time dynamics of the high-dimensional space fractional sine-Gordon equation	9
Dynamics of Newton-like root finding methods	9
A sine transform based preconditioned MINRES method for all-at-once systems from constant and variable-coefficient evolutionary PDEs	9
RBF-FD based some implicit-explicit methods for pricing option under regime-switching jump-diffusion model with variable coefficients	9
Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes	9
An Hermite–Obreshkov method for 2nd-order linear initial-value problems for ODE	9
Anderson accelerating the preconditioned modulus approach for linear complementarity problems on second-order cones	8
The generalized quadrature method for a class of highly oscillatory Volterra integral equations	8
Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations	8
Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces	8
A fast second-order absorbing boundary condition for the linearized Benjamin-Bona-Mahony equation	8
An explicit subgradient extragradient algorithm with self-adaptive stepsize for pseudomonotone equilibrium problems in Banach spaces	8
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	8
Two postprocessing techniques for barycentric rational collocation methods applied to weakly singular VIEs	8
Multivariate quadrature rules on crosslet sparse grids	8
A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling	8
Convergence analysis of Picard–SP iteration process for generalized $$\alpha $$–nonexpansive mappings	8
A minimum-time obstacle-avoidance path planning algorithm for unmanned aerial vehicles	8

Two-level methods for solving higher order finite element discretizations of nonsymmetric and indefinite elliptic problem	8
A method of fundamental solutions for heat and wave propagation from lateral Cauchy data	8
Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems	8
A new proximal-like algorithm for solving split variational inclusion problems	8
TRIPs-Py: Techniques for regularization of inverse problems in python	8
The error estimations of a two-level linearized compact ADI method for solving the nonlinear coupled wave equations	7
Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion	7
The parameterized accelerated iteration method for solving the matrix equation $$AXB=C$$	7
Nitsche’s method for elliptic Dirichlet boundary control problems on curved domains	7
Discussions on a macro multi-time scales coupling method: existence and uniqueness of the numerical solution and strict non-negativity of the Schur complement	7
An adaptively preconditioned multi-step matrix splitting iteration for computing PageRank	7
New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems	7
Efficient high-order exponential time differencing methods for nonlinear fractional differential models	7
A low-rank solution method for Riccati equations with indefinite quadratic terms	7
Complex structure-preserving method for Schrödinger equations in quaternionic quantum mechanics	7
A Tseng extragradient method for solving variational inequality problems in Banach spaces	7
Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples	7
New modulus-based matrix splitting methods for implicit complementarity problem	7
A limited-memory BFGS-based differential evolution algorithm for optimal control of nonlinear systems with mixed control variables and probability constraints	7
On zero behavior of higher-order Sobolev-type discrete $$q-$$Hermite I orthogonal polynomials	7
Bernstein super fractal interpolation function for countable data systems	7
Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries	7
Simultaneous perturbation stochastic approximation: towards one-measurement per iteration	7
Linearly compact scheme for 2D Sobolev equation with Burgers’ type nonlinearity	7
Spurious eigenvalue-free algorithms of the method of fundamental solutions for solving the Helmholtz equation in bounded multiply connected domains	6
Continuation Newton methods with deflation techniques for global optimization problems	6
A new linearized maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation	6
Accelerated methods with fastly vanishing subgradients for structured non-smooth minimization	6
The FMM accelerated PIES with the modified binary tree in solving potential problems for the domains with curvilinear boundaries	6
A high-order numerical scheme for multidimensional convection-diffusion-reaction equation with time-fractional derivative	6
A family of three-term conjugate gradient projection methods with a restart procedure and their relaxed-inertial extensions for the constrained nonlinear pseudo-monotone equations with applications	6
A proper orthogonal decomposition-compact difference algorithm for plate vibration models	6
Detection and correction of silent errors in the conjugate gradient algorithm	6
On an integrated Krylov-ADI solver for large-scale Lyapunov equations	6
Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model	6
A convex splitting method for the time-dependent Ginzburg-Landau equation	6
Certified Newton schemes for the evaluation of low-genus theta functions	6
Orthogonal polynomials relative to a generalized Marchenko–Pastur probability measure	6
Convergence analysis of sample average approximation for a class of stochastic nonlinear complementarity problems: from two-stage to multistage	6
A proximal bundle-based algorithm for nonsmooth constrained multiobjective optimization problems with inexact data	6
Interpretation of parareal as a two-level additive Schwarz in time preconditioner and its acceleration with GMRES	6
Global convergence of a curvilinear search for non-convex optimization	6
A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block	6
On solving 2D weakly singular Volterra integral equations of the second kind	6
An Edge-based cascadic multigrid method for $$H(\textbf{curl})$$ problems	6
Relaxed fixed point iterations for matrix equations arising in Markov chain modeling	6
Automatic approximation using asymptotically optimal adaptive interpolation	6
Uncoupling evolutionary groundwater-surface water flows: stabilized mixed methods in both porous media and fluid regions	6
A fast Fourier-Galerkin method solving boundary integral equations for the Helmholtz equation with exponential convergence	6
On the robustness of exponential base terms and the Padé denominator in some least squares sense	6
Operator-splitting local discontinuous Galerkin method for multi-dimensional linear convection-diffusion equations	6
Spatial two-grid compact difference method for nonlinear Volterra integro-differential equation with Abel kernel	5
Multigrid methods for time fractional conservation laws	5
Generalized weak Galerkin finite element method for linear elasticity interface problems	5
Parallel strategies for Direct Multisearch	5
A fast algorithm for time-fractional diffusion equation with space-time-dependent variable order	5
A Chebyshev-Markov-Stieltjes separation type theorem for classical Romberg quadrature	5
Error profile for discontinuous Galerkin time stepping of parabolic PDEs	5
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters	5
Inverse central ordering for the Newton interpolation formula	5
A matrix splitting preconditioning method for solving the discretized tempered fractional diffusion equations	5
Hybrid iterative refined restarted Lanczos bidiagonalization methods	5
A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation	5
Sharp error estimate of a Grünwald–Letnikov scheme for reaction-subdiffusion equations	5
Extensions of Clenshaw-Curtis-type rules to integrals over a semi-infinite interval	5
A superconvergent ultra-weak local discontinuous Galerkin method for nonlinear fourth-order boundary-value problems	5
A family of linearly weighted-$$\theta $$ compact ADI schemes for sine-Gordon equations in high dimensions	5
A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations	5
A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with structure-preservation for long-time dynamics of the Dirac equation with small potentials	5
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	5
An inertial spectral conjugate gradient projection method for constrained nonlinear pseudo-monotone equations	5
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus	5
ENO-based high-order data-bounded and constrained positivity-preserving interpolation	5
The gamma function via interpolation	5
Numerical analysis of incompressible wormhole propagation with mass-preserving characteristic mixed finite element procedure	5
On the convergence of the numerical blow-up time for a rescaling algorithm	5
A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems	5
Max-convolution through numerics and tropical geometry	5
A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions	5
An hp-version fractional collocation method for Volterra integro-differential equations with weakly singular kernels	5

Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations	5
Positive quadrature formulas on an arc of the unit circle	5
A high-order numerical scheme and its analysis for Caputo temporal-fractional Black-Scholes model: European double barrier knock-out option	5
Improved two-step Newton’s method for computing simple multiple zeros of polynomial systems	5
An effective computational approach based on new multi-step collocation method for solving integral-algebraic equations	4
The backward rounding error analysis of the quaternion Givens QR decomposition	4
A priori and a posteriori error estimation for singularly perturbed delay integro-differential equations	4
C-FISTA type projection algorithm for quasi-variational inequalities	4
A fast stable accurate artificial boundary condition for the linearized Green-Naghdi system	4
A mass- and energy-conserved DG method for the Schrödinger-Poisson equation	4
In reference to a self-referential approach towards smooth multivariate approximation	4
Numerical solution of two-dimensional Hammerstein integral equations via quadratic spline collocation	4
Analytical and numerical solution techniques for a class of time-fractional integro-partial differential equations	4
Detecting and approximating decision boundaries in low-dimensional spaces	4
A highly efficient class of optimal fourth-order methods for solving nonlinear systems	4
Randomized Kaczmarz method with adaptive stepsizes for inconsistent linear systems	4
Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations	4
Extended homogeneous bivariate orthogonal polynomials: symbolic and numerical Gaussian cubature formula	4
Multiscale matrix pencils for separable reconstruction problems	4
Anti-Gaussian quadrature rules related to orthogonality on the semicircle	4
Solving third-order tensor linear complementarity problems via modulus-based methods and applications	4
Generalizing Frobenius inversion to quaternion matrices	4
Globally linearly convergent nonlinear conjugate gradients without Wolfe line search	4
A rotated shift-splitting method for complex symmetric linear systems	4
Differential equation software for the computation of error-controlled continuous approximate solutions	4
Operator-splitting finite element method for solving the radiative transfer equation	4
On the maximal order of convergence of Green’s function method for solving two-point boundary value problems with deviating argument	4
A modified local and parallel finite element method for the coupled Stokes-Darcy model with the Beavers-Joseph interface condition	4
A high-order adaptive numerical algorithm for fractional diffusion wave equation on non-uniform meshes	4
Comment on: “A derivative-free iterative method for nonlinear monotone equations with convex constraints”	4
Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials	4
An ensemble scheme for the numerical solution of a random transient heat equation with uncertain inputs	4
Correction to: Alternatives to the EM algorithm for ML estimation of location, scatter matrix, and degree of freedom of the Student t distribution	4
Richard Steven Varga, 1928–2022	4
Inexact asymmetric forward-backward-adjoint splitting algorithms for saddle point problems	4
Improvements to steepest descent method for multi-objective optimization	4
Implicit–explicit two–step peer methods with RK stability for implicit part	4
Edge importance in complex networks	4
ANODE 2023 In honour of John Butcher’s 90th birthday	4
Correction to: Fitted schemes for Caputo-Hadamard fractional differential equations	4
Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method	4
Variable stepsize general linear methods for ODEs	4
A preconditioned general modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems	4
A second order non-uniform IMEX-Alikhanov-FEM for time-fractional PDEs and PIDEs with time-dependent coefficients	4
Jacobi spectral projection methods for Fredholm integral equations of the first kind	4
Extrapolation methods for multilinear PageRank	4
Accelerated iterative algorithms for the Cauchy problem in steady-state anisotropic heat conduction	4
Two formulae with nodes related to zeros of Bessel functions for semi-infinite integrals: extending Gauss–Jacobi-type rules	4
Local and parallel finite element methods based on two-grid discretizations for the nonstationary Navier-Stokes equations	4
N-mode minimal tensor extrapolation methods	4
Two-dimensional Laplace transform inversion using bivariate homogeneous two-point Padé approximants	4
A numerical approach for solving fractional order pantograph mixed Volterra-Fredholm delay-integro-differential equations	4
RMPIA: a new algorithm for computing the Lagrange matrix interpolation polynomials	4
A reliable numerical algorithm mixed with hypergeometric function for analyzing fractional variational problems	4
Fractal functions associated with Reich contractions: an approximation of chaotic attractors	4
A spatial branch and bound algorithm for solving the sum of linear ratios optimization problem	4
Strong and linear convergence of projection-type method with an inertial term for finding minimum-norm solutions of pseudomonotone variational inequalities in Hilbert spaces	4
$$L^2$$ norm convergence of IMEX BDF2 scheme with variable-step for the incompressible Navier-Stokes equations	4
Fixed-time TGNN model with the nonlinear activation function for online solution of Sylvester tensor equation	4
Iterative methods for solving tensor equations based on exponential acceleration	3
A dynamic distributed conjugate gradient method for variational inequality problem over the common fixed-point constraints	3
A two-level iterative method with Newton-type linearization for the stationary micropolar fluid equations	3
A μ-mode BLAS approach for multidimensional tensor-structured problems	3
Optimality and duality results for fractional programming problems under E-univexity	3
Modified iterated Crank-Nicolson method with improved accuracy for advection equations	3
An EMC-HDG scheme for the convection-diffusion equation with random diffusivity	3
Completely discrete schemes for 2D Sobolev equations with Burgers’ type nonlinearity	3
Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation	3
Subspace method for the estimation of large-scale structured real stability radius	3
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models	3
Generalized second derivative linear multistep methods for ordinary differential equations	3
Analytic evaluation of the FCC Voronoi-splines	3
On the L$$^{\infty }$$ convergence of a novel fourth-order compact and conservative difference scheme for the generalized Rosenau-KdV-RLW equation	3
A mixed precision LOBPCG algorithm	3
Deviation maximization for rank-revealing QR factorizations	3
A note on stability and fractal dimension of bivariate α-fractal functions	3
Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators	3
On semilocal convergence analysis for two-step Newton method under generalized Lipschitz conditions in Banach spaces	3
Novel numerical methods based on graded, adaptive and uniform meshes for a time-fractional advection-diffusion equation subjected to weakly singular solution	3
Fast and stable rational approximation of generalized hypergeometric functions	3
Extrapolation quadrature from equispaced samples of functions with jumps	3
$$O(1/k^2)$$ convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming	3
A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting	3
A Lanczos-type procedure for tensors	3
Analysis of a New Krylov subspace enhanced parareal algorithm for time-periodic problems	3
Arbitrarily high-order energy-conserving methods for Poisson problems	3
The finite steps of convergence of the fast thresholding algorithms with f-feedbacks in compressed sensing	3
Error analysis for the pseudostress formulation of unsteady Stokes problem	3
Computation of polynomial and rational approximations in complex domains by the $$\tau $$-method	3
An efficient numerical method on modified space-time sparse grid for time-fractional diffusion equation with nonsmooth data	3
Block GPBi-CG method for solving nonsymmetric linear systems with multiple right-hand sides and its convergence analysis	3
Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime	3
Total positivity and accurate computations with Gram matrices of Bernstein bases	3
A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners	3
Upper triangulation-based infinity norm bounds for the inverse of Nekrasov matrices with applications	3