相关论文: An efficient third-order scheme for BSDEs based on…

In this paper we construct high order numerical methods for solving third and fourth orders nonlinear functional differential equations (FDE). They are based on the discretization of iterative methods on continuous level with the use of the…

New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…

In this paper, we study the connections between three concepts - the reverse H\"older inequality for matrix-valued martingales, the well-posedness of linear BSDEs with unbounded coefficients, and the well-posedness of quadratic BSDE…

We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) for the $n$-dimensional non-homogeneous wave equation, $n\geq 1$. Their construction is accomplished by both the…

We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…

We consider an implicit finite difference scheme on uniform grids in time and space for the Cauchy problem for a second order parabolic stochastic partial differential equation where the parabolicity condition is allowed to degenerate. Such…

We present a second-order ensemble method based on a blended three-step backward differentiation formula (BDF) timestepping scheme to compute an ensemble of Navier-Stokes equations. Compared with the only existing second-order ensemble…

In this paper, we present and analyse a class of "filtered" numerical schemes for second order Hamilton-Jacobi-Bellman equations. Our approach follows the ideas introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes for the…

In this paper we present two numerical schemes of approximating solutions of backward doubly stochastic differential equations (BDSDEs for short). We give a method to discretize a BDSDE. And we also give the proof of the convergence of…

Stochastic differential equations (sdes) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes…

We introduce a new class of "filtered" schemes for some first order non-linear Hamilton-Jacobi-Bellman equations. The work follows recent ideas of Froese and Oberman (SIAM J. Numer. Anal., Vol 51, pp.423-444, 2013). The proposed schemes are…

In this paper we study different algorithms for reflected backward stochastic differential equations (BSDE in short) with two continuous barriers basing on random work framework. We introduce different numerical algorithms by penalization…

As is well-known, the advantage of the high-order compact difference scheme (H-OCD) is unconditionally stable and convergent with the order $O(\tau^2+h^4)$ under the maximum norm. In this article, a new numerical gradient scheme based on…

In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We…

First-order fully implicit as well as implicit--explicit schemes for coupled elliptic-parabolic systems are discussed in [Ern and Meunier, ESAIM: M2AN, 2009] and [Altmann et al., Math.\ Comp., 2021], respectively. The extension of the…

In this work, we construct a fifth-order weighted essentially non-oscillatory (WENO) scheme with exponential approximation space for solving dispersive equations. A conservative third-order derivative formulation is developed directly using…

How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…

The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…

This paper is dedicated to the construction of high-order (in both space and time) finite-difference schemes for both forward and backward PDEs and PIDEs, such that option prices obtained by solving both the forward and backward equations…

We introduce an efficient and accurate staggered-grid finite-difference (SGFD) method to solve the two-dimensional elastic wave equation. We use a coupled first-order stress-velocity formulation. In the standard implementation of SGFD…