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A highly accurate method for simulating surfactant-covered droplets in two-dimensional Stokes flow with solid boundaries is presented. The method handles both periodic channel flows of arbitrary shape and stationary solid constrictions. A…
Initial-boundary value problems for 1-dimensional `completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures. A fundamental step in any typical iterative inversion method, is the numerical solution of the underlying direct…
A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous…
We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods.…
This study analyzes steady periodic hydroelastic waves propagating on the water surface of finite depth beneath nonlinear elastic membranes. Unlike previous work \cite{BaldiT,BaldiT1,Toland,Toland1}, our formulation accommodates rotational…
The aim of this study is to present a reliable combination of the differential transformation method (DTM) and Pad\'e approximants to make, for the first time, a semi-analytic analysis of the problem of free convection boundary-layer flow…
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…
In this paper, we define a non-iterative transformation method for boundary-layer flows of non-Newtonian fluids past a flat plate. The problem to be solved is an extended Blasius problem depending on a parameter. This method allows us to…
We study the local and global wellposedness of the initial-boundary value problem for the biharmonic Schr\"odinger equation on the half-line with inhomogeneous Dirichlet-Neumann boundary data. First, we obtain a representation formula for…
The broadband line-by-line analysis of radiative transfer in the atmosphere is extremely demanding with regard to computational resources. As a remedy, we present here the calculation of uniform error bounds for approximating the classical…
We present a fully analytic approach for evaluating boundary integrals in two dimensions for Smoothed Particle Hydrodynamics (SPH). Conventional methods often rely on boundary particles or wall re-normalization approaches derived from…
Richards equation is often used to represent two-phase fluid flow in an unsaturated porous medium when one phase is much heavier and more viscous than the other. However, it cannot describe the fully saturated flow for some capillary…
We propose a geometric approach for the numerical integration of singular initial value problems for (systems of) quasi-linear differential equations. It transforms the original problem into the problem of computing the unstable manifold at…
The present study aims to extend the applicability of the static-boundary absorption method in phase-resolving CFD simulations outside the conventional shallow-water waves limit. Even though this method was originally formulated for…
This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect…
In this work, we consider a mathematical model for flow in a unsaturated porous medium containing a fracture. In all subdomains (the fracture and the adjacent matrix blocks) the flow is governed by Richards' equation. The submodels are…
The isometric embedding problem is a fundamental problem in differential geometry. A longstanding problem is considered in this paper to characterize intrinsic metrics on a two-dimensional Riemannian manifold which can be realized as…
We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…