## Numerical Algorithms OnlineFirst articles

15-11-2020 | Original Paper

### Modified third and fifth order WENO schemes for inviscid compressible flows

The weighted essentially non-oscillatory schemes are well known for their shock captu- ring abilities due to their properties resulting from weighted combination reconstruction taken such that less weight is given to less smooth stencils. In this …

13-11-2020 | Original Paper

### Local and parallel finite element algorithms for the time-dependent Oseen equations

Based on two-grid discretizations, local and parallel finite element algorithms are proposed and analyzed for the time-dependent Oseen equations. Using conforming finite element pairs for the spatial discretization and backward Euler scheme for …

13-11-2020 | Original Paper

### Interpolation of sparse high-dimensional data

Increases in the quantity of available data have allowed all fields of science to generate more accurate models of multivariate phenomena. Regression and interpolation become challenging when the dimension of data is large, especially while …

12-11-2020 | Original Paper

### Wavelet regularization strategy for the fractional inverse diffusion problem

This manuscript deals with an inverse fractional-diffusing problem, the time-fractional heat conduction equation, which is a physical model of a problem, where one needs to identify the temperature distribution of a semi-conductor, but one …

06-11-2020 | Original Paper

### α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation

An initial-boundary value problem of the form D t α u + Δ 2 u − c Δ u = f ${D}_{t}^{\alpha } u+{\varDelta }^{2}u-c{\varDelta } u =f$ is considered, where D t α ${D}_{t}^{\alpha }$ is a Caputo temporal derivative of order α ∈ (0,1) and c is a …

05-11-2020 | Original Paper

### Derivative-free superiorization: principle and algorithm

The superiorization methodology is intended to work with input data of constrained minimization problems, that is, a target function and a set of constraints. However, it is based on an antipodal way of thinking to what leads to constrained …

30-10-2020 | Original Paper

### A stable minimal search method for solving multi-order fractional differential equations based on reproducing kernel space

In this paper, a stable minimal search method based on reproducing kernel space is proposed for solving multi-order fractional differential equations. The existence and uniqueness of solution of the considered equation is proved and the smoothness …

30-10-2020 | Original Paper

### A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation

The ‘equation-free toolbox’ empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable scientists and engineers to immediately use microscopic simulators to perform macro-scale system level tasks and analysis …

30-10-2020 | Original Paper

### Spectral collocation method for Caputo fractional terminal value problems

Spectral collocation method is proposed to solve Caputo fractional terminal value problem. The main idea of the proposed method is to solve the corresponding nonlinear weakly singular Volterra-Fredholm integral equation. The key step in presented …

29-10-2020 | Original Paper

### An arc-search infeasible interior-point method for semidefinite optimization with the negative infinity neighborhood

We present an arc-search infeasible interior-point algorithm for semidefinite optimization using the Nesterov-Todd search directions. The algorithm is based on the negative infinity neighborhood of the central path. The algorithm searches an …

28-10-2020 | Original Paper

### A fast solver of Legendre-Laguerre spectral element method for the Camassa-Holm equation

An efficient and accurate Legendre-Laguerre spectral element method for solving the Camassa-Holm equation on the half line is proposed. The spectral element method has the flexibility for arbitrary h and p adaptivity. Two kinds of Sobolev …

28-10-2020 | Original Paper

### New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization

In this paper, two new subspace minimization conjugate gradient methods based on p-regularization models are proposed, where a special scaled norm in p-regularization model is analyzed. Different choices of special scaled norm lead to different …

26-10-2020 | Original Paper

### Analysis of an adaptive collocation solution for retarded and neutral delay systems

This paper introduces an adaptive collocation method to solve retarded and neutral delay differential equations (RDDEs and NDDEs) with constant or time-dependent delays. The delays are allowed to be small or become vanishing during the …

25-10-2020 | Original Paper

### On preconditioning and solving an extended class of interval parametric linear systems

We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously, we want this enclosure to be tight and cheap to …

24-10-2020 | Original Paper

### New degrees of freedom for high-order Whitney approximations of Darcy’s flows

We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. We propose a high-order discretisation based on Whitney finite elements, namely, Raviart-Thomas finite elements of degree r + 1 for the discharge and …

19-10-2020 | Original Paper

### Local and parallel finite element methods for the coupled Stokes/Darcy model

In this paper, based on two-grid discretizations, two kinds of local and parallel finite element methods are proposed and investigated for the coupled Stokes/Darcy model. Following the idea presented in Xu and Zhou (Math. Comput. 69, 881–909 …

18-10-2020 | Original Paper

### Asynchronous Richardson iterations: theory and practice

We consider asynchronous versions of the first- and second-order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values are chosen a priori. We explore the parameter values that can be proven to …

15-10-2020 | Original Paper

### An algorithm based on QSVD for the quaternion equality constrained least squares problem

Quaternion equality constrained least squares (QLSE) problems have attracted extensive attention in the field of mathematical physics due to its applicability as an extremely effective tool. However, the knowledge gap among numerous QLSE problems …

14-10-2020 | Original Paper

### Second derivative backward differentiation formulae for ODEs based on barycentric rational interpolants

For their several attractive features from the viewpoint of the numerical computations, linear barycentric rational interpolants have been recently used to construct various numerical methods for solving different classes of equations. In this …

10-10-2020 | Original Paper

### Waveform relaxation for fractional sub-diffusion equations

We report a new kind of waveform relaxation (WR) method for general semi-linear fractional sub-diffusion equations, and analyze the upper bound for the iteration errors. It indicates that the WR method is convergent superlinearly, and the …