Related papers: On the Stability of Some Spline Collocation Implic…
We develop a local polynomial spline interpolation scheme for arbitrary spline order on bounded intervals. Our method's local formulation, effective boundary considerations and optimal interpolation error rate make it particularly useful…
A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…
In this paper we show how to construct diagonal scalings for arbitrary matrix pencils $\lambda B-A$, in which both $A$ and $B$ are complex matrices (square or nonsquare). The goal of such diagonal scalings is to "balance" in some sense the…
Although Galerkin discretizations have been intensively employed in the IgA context, an efficient implementation requires special numerical quadrature rules when constructing the system of equations. To avoid this issue, isogeometric…
In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using…
In this paper, we introduce and analyse numerical schemes for the homogeneous and the kinetic L\'evy-Fokker-Planck equation. The discretizations are designed to preserve the main features of the continuous model such as conservation of…
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…
In this paper, a well-conditioned collocation method is constructed for solving general $p$-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of…
A characterization of the structure of a regular matrix pencil obtained by a bounded rank perturbation of another regular matrix pencil has been recently obtained. The result generalizes the solution for the bounded rank perturbation…
In this paper we introduce a procedure, based on the method of equivariant moving frames, for formulating continuous Galerkin finite element schemes that preserve the Lie point symmetries of initial value problems for ordinary differential…
Closed subschemes in projective space with a fixed Hilbert polynomial are parametrized by a Hilbert scheme. We classify the smooth ones. We identify numerical conditions on a polynomial that completely determine when the Hilbert scheme is…
We study a second order scheme for spatial fractional differential equations with variable coefficients. Previous results mainly concentrate on equations with diffusion coefficients that are proportional to each other. In this paper, by…
Motivated by the ubiquitous sampled-data setup in applied control, we examine the stability of a class of difference equations that arises by sampling a right- or left-invariant flow on a matrix Lie group. The map defining such a difference…
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
An accurate system to study the stability of pipe flow that ensures regularity is presented. The system produces a spectrum that is as accurate as Meseguer \& Trefethen (2000), while providing flexibility to amend the boundary conditions…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
The aim of this paper is to propose a new method for numerical approximations of the solution of the linear stochastic partial differential equation arising in non-linear filtering problems: the Zaka\"i equation. The approximation scheme is…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
In this paper, we prove that, under precise spectral assumptions, some finite difference approximations of scalar leftgoing transport equations on the positive half-line with numerical boundary conditions are $\ell^1$-stable but…
The method of equivariant moving frames on multi-space is used to construct symmetry preserving finite difference schemes of partial differential equations invariant under finite-dimensional symmetry groups. Invariant numerical schemes for…