Related papers: Fourth order accurate compact scheme for first-ord…
For a general nonlinear control system, we study the problem of small time local attainability of a target which is the closure of an open set. When the target is smooth and locally the sublevel set of a smooth function, we develop second…
This manuscript introduces a fourth-order Runge-Kutta based implicit-explicit scheme in time along with compact fourth-order finite difference scheme in space for the solution of one-dimensional Kuramoto-Sivashinsky equation with periodic…
We propose a second-order implicit-explicit (IMEX) time-stepping scheme for the isentropic, compressible Cahn-Hilliard-Navier-Stokes equations discretized on staggered (MAC) grids. The scheme is based on finite difference approximations…
We propose an adaptive stencil construction for high order accurate finite volume schemes aposteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations. High-accuracy (up to the sixth-order presently) is achieved…
This paper presents compact, symmetric, and high-order finite difference methods (FDMs) for the variable Poisson equation on a $d$-dimensional hypercube. Our scheme produces a symmetric linear system: an important property that does not…
In this paper, a compact third-order gas-kinetic scheme is proposed for the compressible Euler and Navier-Stokes equations. The main reason for the feasibility to develop such a high-order scheme with compact stencil, which involves only…
For the recently introduced algorithms to solve the time-dependent Maxwell equations (see Phys.Rev.E Vol.64 p.066705 (2001)), we construct a variable grid implementation and an improved spatial discretization implementation that preserve…
Many applications involve partial differential equations which admits nontrivial steady state solutions. The design of schemes which are able to describe correctly these equilibrium states may be challenging for numerical methods, in…
We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…
Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithm conserves a discrete non-canonical symplectic structure…
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems. In this way we develop an approach to a class of fourth order elliptic partial differential equations using the idea of splitting into…
In an attempt to solve Maxwell's first order system of equations, starting from a given initial state, it is found that a consistent solution depending on the temporal evolution of the sources cannot be calculated. The well known retarded…
We establish several sufficient conditions for the strong ellipticity of any fourth-order elasticity tensor in this paper. The first presented sufficient condition is an extension of positive definite matrices, which states that the strong…
A numerical scheme is described for accurately accommodating oblique, non-aligned, boundaries, on a three-dimensional cartesian grid. The scheme gives second-order accuracy in the solution for potential of Poisson's equation using compact…
Schemes with the second-order approximation in time are considered for numerical solving the Cauchy problem for an evolutionary equation of first order with a self-adjoint operator. The implicit two-level scheme based on the Pad\'{e}…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an…
We present a new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions. In the spirit of Godunov-type schemes,our method is based on reconstructing a piecewise-polynomial…
We consider solid state phase transformations that are caused by free energy densities with domains of non-convexity in strain-composition space; we refer to the non-convex domains as mechano-chemical spinodals. The non-convexity with…
We propose a second-order implicit-explicit (IMEX) time-stepping scheme for the isentropic, compressible Cahn-Hilliard-Navier-Stokes equations in the low Mach number regime. The method is based on finite differences on staggered grids and…