Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems.

The goal of this work is to determine classes of traveling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz.

We develop a new efficient second-order finite difference scheme for two-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows that the scheme is second-order convergence in the L2 norm and is unconditionally stable. Numerical results demonstrate that the error measures of the second-order scheme are several times smaller than those of the standard implicit finite d...

We characterize orthogonal matrix polynomials (Pn)n whose differences (∇ Pn+1)n are also orthogonal by means of a discrete Pearson equation for the weight matrix W with respect to which the polynomials (Pn)n are orthogonal. We also construct some illustrative examples. In particular, we show that contrary to what happens in the scalar case, in the matrix orthogonality the discrete Pearson equat...

This paper describes a technique for timestamping data from an array of sensors. This is a challenging issue that needs to be solved for the magnetometry-based navigation system presented here. This system uses finite difference schemes to evaluate spatial and time derivatives of a vector field. The accuracy of the timestamping method is critical. In the context of this particular application, ...

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We study a superreplication problem of European options with gamma constraints, in mathematical finance. The initially unbounded control problem is set back to a problem involving a viscosity PDE solution with a set of bounded controls. Then a numerical approach is introduced, inconditionnally stable with respect to the mesh steps. A generalized finite difference scheme is used since basic fini...

Thirdand fourth-order accurate finite difference schemes for the first derivative of the square of the speed are developed, for both uniform and non-uniform grids, and applied in the study of a two-dimensional viscous fluid flow through an irregular domain. The von Mises transformation is used to transform the governing equations, and map the irregular domain onto a rectangular computational do...

Finite difference method is used to calculate the via-plate capacitances for vias with pad. Due to the symmetric structure, the solving domain is reduced to a rectangular ρ − z region. Boundary conditions along the region are discussed. Both barrel-plate and pad-plate capacitances are studied with various geometric parameters. The results could be used as validations for possible analytical exp...

Discrete versions of basic inequalities in functional analysis such as the Sobolev inequality play key role in theoretical analysis of finite difference schemes. They have been shown for some simple difference operators, but are still left open for general operators, even including the standard central difference operators. In this paper, we propose a systematic approach for deriving such inequ...