相关论文: On numerical solutions to stochastic Volterra equa…

Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…

The conforming finite element Galerkin method is applied to discretise in the spatial direction for a class of strongly nonlinear parabolic problems. Using elliptic projection of the associated linearised stationary problem with Gronwall…

A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…

We develop a stable and high-order accurate discontinuous Galerkin method for the second order wave equation, specifically designed to handle nonsmooth solutions. Our approach integrates the energy-based discontinuous Galerkin method with…

The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. The novel idea of weak Galerkin finite element methods is on the use of weak functions and…

A new parallel solver for the volumetric integral equations (IE) of electrodynamics is presented. The solver is based on the Galerkin method which ensures the convergent numerical solution. The main features include: (i) the memory usage is…

We use a finite element approach based on Galerkin method to obtain approximate steady state solutions of the thermistor problem with temperature dependent electrical conductivity.

In this work we consider a simple, approximate, tending toward exact, solution of the system of two usual Lotka-Volterra differential equations. Given solution is obtained by an iterative method. In any finite approximation order of this…

The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize…

The sufficient conditions are obtained for existence of the main solution of the nonlinear Volterra integral equation of the second kind on the semi-axis and on a finite interval. The method for computation of this boundary interval is…

The finite element method, finite difference method, finite volume method and spectral method have achieved great success in solving partial differential equations. However, the high accuracy of traditional numerical methods is at the cost…

Numerical solution of nonlocal constrained value problems with integrable kernels are considered. These nonlocal problems arise in nonlocal mechanics and nonlocal diffusion. The structure of the true solution to the problem is analyzed…

Markov expanding maps, a class of simple chaotic systems, are commonly used as models for chaotic dynamics, but existing numerical methods to study long-time statistical properties such as invariant measures have a poor trade-off between…

This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…

This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework…

In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By…

We outline two alternative schemes to perform numerical calculations in quantum field theory. In principle, both of these approaches are better suited to study phase structure than conventional Monte Carlo. The first method, Source…

The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov--Poisson equation. Since these methods are conservative, local in space, and able to limit numerical…

A new computational idea for continuum quantum field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating…

Numerical algorithms for the integration of stochastic differential equations in the presence of white noise are introduced and compared. Algorithms for the integration of stochastic correlated forces are also briefly reviewed. Finally, a…