Related papers: A new series solution method for the transmission …
Multitrace formulations (MTFs) are based on a decomposition of the problem domain into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous mathematical MTF can however be daunting for the non-specialist. We…
By means of the Ito-Nisio theorem, we introduce and discuss a general approach to series representations of path integrals. We then argue that the optimal basis for both ``primitive'' and partial averaged approaches is the Wiener…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
The transmission eigenvalue problem (TEP) plays a central role in inverse scattering theory. Despite substantial theoretical progress, the numerical solution of direct and inverse TEP in spherically symmetric domains with variable…
We establish a strategy for finding sharp upper and lower numerical bounds of the Poincar\'e constant on a class of planar domains with piecewise self-similar boundary. The approach consists of four main components: W1) tight inner-outer…
We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of…
In the framework of the Laplacian transport, described by a Robin boundary value problem in an exterior domain in $\mathbb{R}^n$, we generalize the definition of the Poincar\'e-Steklov operator to $d$-set boundaries, $n-2< d<n$, and give…
We numerically examine the exterior solution of spherically symmetric and static configuration in scalar-tensor theories by using the nonminimally coupled scalar field with zero potential as our sample model. Our main purpose in this work…
We reexamine the external field problem for $N\times N$ hermitian one-matrix models. We prove an equivalence of the models with the potentials $\tr{({1/over2N}X^2 + \log X - \Lambda X)}$ and $\sum_{k=1}^\infty t_k\tr{X^k}$ providing the…
In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…
In the present paper we describe a class of algorithms for the solution of Laplace's equation on polygonal domains with Neumann boundary conditions. It is well known that in such cases the solutions have singularities near the corners which…
This article provides a general iterative approximation to partial differential equations, and thus establish existence of smooth solution. The heart of the method is to contract (or expand) the boundary conditions uniformly in the domain,…
In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…
A method for approximate solution of initial value and spectral problems for one dimensional Dirac equation based on an analytic approximation of the transmutation operator is presented. In fact the problem of numerical approximation of…
This work addresses the imposition of outflow boundary conditions for one-dimensional conservation laws. While a highly accurate numerical solution can be obtained in the interior of the domain, boundary discretization can lead to…
We demonstrate that solving the classical problems mentioned in the title on quadrature domains when the given boundary data is rational is as simple as the method of partial fractions. A by-product of our considerations will be a simple…
We study the global hypoellipticity and solvability of strongly invariant operators and systems of strongly invariant operators on closed manifolds. Our approach is based on the Fourier analysis induced by an elliptic pseudo-differential…
In this paper we propose a new formulation of the Fourier Modal Method based on an alternative treatment of interface conditions allowing us to overcome the effect of the Gibbs phenomenon. Explicit consideration of the interface conditions…
In this work we present a power series method for solving ordinary and partial differential equations. To demonstrate our method we solve a system of ordinary differential equations describing the movement of a random walker on a…
This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data. This theory finds applications in multi-wave imaging, greedy methods to…