相关论文: Preconditioning fractional spectral collocation

We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…

Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…

Interval approaches for the reachability analysis of initial value problems for sets of classical ordinary differential equations have been investigated and implemented by many researchers during the last decades. However, there exist…

We consider the solution of systems of linear algebraic equations (SLAEs) with an ill-conditioned or degenerate exact matrix and an approximate right-hand side. An approach to solving such a problem is proposed and justified, which makes it…

Stiff hyperbolic balance laws exhibit large spectral gaps, especially if the relaxation term significantly varies in space. Using examples from rarefied gases and the general form of the underlying balance law model, we perform a detailed…

This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…

We present a stochastic method for efficiently computing the solution of time-fractional partial differential equations (fPDEs) that model anomalous diffusion problems of the subdiffusive type. After discretizing the fPDE in space, the…

We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure…

The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…

An all-at-once linear system arising from the nonlinear tempered fractional diffusion equation with variable coefficients is studied. Firstly, the nonlinear and linearized implicit schemes are proposed to approximate such the nonlinear…

A spectral solution method is proposed to solve a previuously developed non-equilibrium statistical model describing partial thermalization of produced charged hadrons in relativistic heavy-ion collisions, thus improving the accuracy of the…

Interior point methods solve small to medium sized problems to high accuracy in a reasonable amount of time. However, for larger problems as well as stochastic problems, one needs to use first-order methods such as stochastic gradient…

Spectral deferred corrections (SDC) are a class of iterative methods for the numerical solution of ordinary differential equations. SDC can be interpreted as a Picard iteration to solve a fully implicit collocation problem, preconditioned…

Several kernel-based methods for the numerical solution of fractional differential equations have been developed in the recent past; however, these techniques exclusively relied on the use of radial basis function approximations. In the…

Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional…

Partial differential equations (PDEs) involving fractional Laplace operators have been increasingly used to model non-local diffusion processes and are actively investigated using both analytical and numerical approaches. The purpose of…

Immersed finite element methods generally suffer from conditioning problems when cut elements intersect the physical domain only on a small fraction of their volume. De Prenter et al. [Computer Methods in Applied Mechanics and Engineering,…

The radiation condition is the key question in the mathematical modelling for scattering problems in unbounded domains. Mathematically, it plays the role as the "boundary condition" at the infinity, which guarantees the well-posedness of…

In this paper, we consider spectral-collocation method base on Legendre-Gauss-Lobatto point. We present a computational method for solving a class of fractional integral equation of the second kind. Then based on Legendre-Gauss-Lobatto…

System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…