相关论文: Numerical Methods for the Nonlocal Wave Equation o…

Peridynamics formulates the balance of linear momentum as an integro-differential equation, making it naturally suited for fracture modeling without special treatment of discontinuities. The bond-associated correspondence formulation…

We study a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that…

In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…

A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…

A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…

A partial differential equation model is analyzed for the two-slit experiment of quantum mechanics. The state variable of the equation is the probability density function of particle positions. The equation has a diffusion term…

We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…

This paper presents a novel approach for numerical solution of a class of fourth order time fractional partial differential equations (PDE's). The finite difference formulation has been used for temporal discretization, whereas, the space…

We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…

This work considers the nodal finite element approximation of peridynamics, in which the nodal displacements satisfy the peridynamics equation at each mesh node. For the nonlinear bond-based peridynamics model, it is shown that, under the…

This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The proposed methods are natural extensions of well-known…

The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic…

This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretization, we introduce an auxiliary variable analogous to the…

A fifth--order nonlinear partial differential equation for the description of nonlinear waves in a liquid with gas bubbles is considered. Special solutions of this equation are studied. Some elliptic and simple periodic traveling waves…

Piezoelectric appliances have become hugely important in the past century and computer simulations play an essential part in the modern design process thereof. While much work has been invested into the practical simulation of piezoelectric…

Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…

We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference schemes are nonlinearly unstable. We build convergent finite…

We present a new parallel numerical method for solving the non-stationary Schr\"odinger equation with linear nonlocal condition and time-dependent potential which does not commute with the stationary part of the Hamiltonian. The given…

In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…