相关论文: The numerical solutions of linear semi-discrete ev…
We study the convergence of semilinear parabolic stochastic evolution equations, posed on a sequence of Banach spaces approximating a limiting space and driven by additive white noise projected onto the former spaces. Under appropriate…
In this paper, we study an evolution equation that involves a half-Laplacian operator derived from the Riesz fractional Laplacian, combined with a differential operator \(\mathcal{L}\). Using the identity $(-\Delta)^{1/2}=\mathcal…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…
We consider semilinear evolution equations for which the linear part generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces. In this setting, we prove the existence of solutions…
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly employed in the related…
We evaluate the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations. The methods are based on affine combinations of time-splitting integrators and…
We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods.…
This paper studies the convergence of a spatial semi-discretization for a backward semilinear stochastic parabolic equation. The filtration is general, and the spatial semi-discretization uses the standard continuous piecewise linear…
This paper studies the convergence of three temporal semi-discretizations for a backward semilinear stochastic evolution equation. For general terminal value and general coefficient with Lipschitz continuity, the convergence of the first…
In this paper, we introduce a new nonlinear evolution partial differential equation for sparse deconvolution problems. The proposed PDE has the form of continuity equation that arises in various research areas, e.g. fluid dynamics and…
This paper develops and analyzes a semi-discrete and a fully discrete finite element method for a one-dimensional quasilinear parabolic stochastic partial differential equation (SPDE) which describes the stochastic mean curvature flow for…
We develop a fully discrete, semi-implicit mixed finite element method for approximating solutions to a class of fourth-order stochastic partial differential equations (SPDEs) with non-globally Lipschitz and non-monotone nonlinearities,…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the…
We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In…
The objective of this work is to present the existence result for the evolu- tionary compressible Navier-Stokes equations via time discretization. We consider the two-dimensional case with slip boundary conditions. First, the existence of…
In [Proc. Roy. Soc. London Ser. A 453 (1997), no. 1962, 1411-1443] A.S. Fokas introduced a novel method for solving a large class of boundary value problems associated with evolution equations. This approach relies on the construction of a…
We use the semi-discrete method, originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics, 89(6), to reproduce qualitative…
We analyze a generalization of the sine-Gordon equation in laboratory coordinates on the half-line. Using the Fokas transform method for the analysis of initial-boundary value problems for integrable PDEs, we show that the solution $u(x,t)$…