The two-dimensional problem of advection–dispersion associated with a non-aqueousphase liquid (NAPL) pool is addressed using the boundary element method. The problem is appropriately posed with an inhomogeneous boundary condition taking into consideration the presence of the pool and the impermeable layer. We derive a Fredholm integral equation of the first kind for the concentration gradient a...

We consider a boundary value problem for the time-dependent Oseen system in a 3D exterior domain. This problem is reduced to an integral equation for the single-layer potential related to the that system. This integral equation, in turn, is solved by applying a result by Shen [11] pertaining to the evolutionary Stokes system. Since it automatically leads to an integral representation of the sol...

In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...

In this paper, we present an efficient method for determining the solution of the stochastic second kind Volterra integral equations (SVIE) by using the Taylor expansion method. This method transforms the SVIE to a linear stochastic ordinary differential equation which needs specified boundary conditions. For determining boundary conditions, we use the integration technique. This technique give...

Abstract. In this paper, we consider the harmonic extension problem, which is widely used in many applications of machine learning. We formulate the harmonic extension as solving a LaplaceBeltrami equation with Dirichlet boundary condition. We use the point integral method (PIM) proposed in [14, 19, 13] to solve the Laplace-Beltrami equation. The basic idea of the PIM method is to approximate t...

Keywords: Stefan problem Non-classical heat equation Free boundary problem Similarity solution Nonlinear heat sources Volterra integral equation a b s t r a c t We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a convective boundary condition at the fixed face x = 0. Here the he...

s of IWANASP, October 22 – 24, 2015, Lagos, Portugal A FAST FOURIER–GALERKIN METHOD SOLVING A BOUNDARY INTEGRAL EQUATION FOR THE BIHARMONIC EQUATION

We consider mixed boundary value problems in Physical Geodesy and study possibilities in order to transform them into a system of integral equations over the boundary of the domain. The system of integral equations can be solved numerically, by, e.g. boundary element methods, provided that (a) the mixed boundary value problem is uniquely solvable, (b) the system of integral equations is equival...

The optimal exercise boundary near the expiration time is determined for an American put option. It is obtained by using Green's theorem to convert the boundary value problem for the price of the option into an integral equation for the optimal exercise boundary. This integral equation is solved asymptotically for small values of the time to expiration. The leading term in the asymptotic soluti...

The logarithmic capacity of compact sets in R2 plays an important role in various fields of applied mathematics. Its value can be computed analytically for a few simple sets. In this paper a new algorithm is presented that numerically approximates the logarithmic capacity for more involved sets. The algorithm requires the solution of a boundary integral equation with Dirichlet boundary data. Th...