In this article, we devote ourselves to establishing a natural boundary element (NBE) method for the Sobolev equation in the 2D unbounded domain. To this end, we first constitute the time semi-discretized super-convergence format for the Sobolev equation by means of the Newmark method. Then, using the principle of natural boundary reduction, we establish a fully discretized NBE format based on ...

We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the existence of a global branch of nonnegative stationary states, covering both the cases of a bounded and an unbounded domain. The global bifurcation of stationary states, implies-in conjuction with the definition of a g...

The phase flow method was originally introduced in [28] which can efficiently solve autonomous ordinary differential equations. In [13], the method was generalized to solve Hamiltonian system where the Hamiltonian function was discontinuous. However, both these methods require phase flow map constructed on an invariant manifold. This can increase computational cost when the invariant domain is ...

In this paper, we prove a maximum principle for the general multi-term space-time-fractional transport equation and apply it establishing uniqueness of solution to an initial-boundary-value problem equation. We also derive some comparison principles solutions problems with different data. Finally, present Cauchy time-fractional on unbounded domain.

The goal of unbounded program verification is to discover an inductive invariant that safely over-approximates all possible program behaviors. Functional languages featuring higher order and recursive functions become more popular due to the domain-specific needs of big data analytics, web, and security. We present Rosette/Unbound, the first program verifier for Racket exploiting the automated ...

Array constraints are essential for handling data structures in automated reasoning and software verification. Unfortunately, the use of a typical finite domain (FD) solver based on local consistencybased filtering has strong limitations when constraints on indexes are combined with constraints on array elements and size. This paper proposes an efficient and complete FD-solving technique for ex...

We consider the impact of additive Gaussian white noise on a supercritical pitchfork bifurcation in an unbounded domain. As example we focus stochastic Swift-Hohenberg equation with polynomial nonlinearity. Here identify order where small first impacts bifurcation. Using approximation via modulation equations, provide tool to analyse how influences dynamics close change stability.

In this paper we extend the source transfer domain decomposition method (STDDM) introduced by the authors to solve the Helmholtz problems in two-layered media, the Helmholtz scattering problems with bounded scatterer, and Helmholtz problems in 3D unbounded domains. The STDDM is based on the decomposition of the domain into non-overlapping layers and the idea of source transfer which transfers t...

Abstract. We propose and study a domain decomposition method for solving the truncated perfectly matched layer (PML) approximation in bounded domain of Helmholtz scattering problems. The method is based on the decomposition of the domain into non-overlapping layers and the idea of source transfer which transfers the sources equivalently layer by layer so that the solution in the final layer can...

The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context time-domain electromagnetic wave propagation a 3D unbounded anisotropic homogeneous medium modelled by diagonal dielectric tensor is presented. Contrary to scalar equation or 2D Maxwell’s equations some anisotropies lead existence backward waves giving rise instabilities PMLs. Numerical experiments confirm presented result.