The performance of the boundary and finite element methods for the Helmholtz equation in two dimensions is investigated. To facilitate the comparison, the system of linear equations arising from the finite element formulation is reduced to a smaller system involving the boundary values of the unknown function and its normal derivative alone. The difference between the boundary and finite elemen...

The ultimate goal of this research is to construct a hybrid model for sound propagation in layered underwater environments with curved boundaries by employing a di↵erential formulation for inhomogeneous layers and a boundary integral formulation for homogeneous layers. The discretization of the new hybrid model is a combination of a finite di↵erence method for the Helmholtz equation for inhomog...

This paper presents a boundary integral equation method for computing numerical conformal mapping of bounded multiply connected region onto an annulus with spiral slits region and its inverse. The method is an extension of the author’s method for computing the Annulus with circular slits map of bounded multiply connected regions (see [Sangawi, A. W. K., Murid, A. H. M., Nasser, M. M. S.: Annulu...

We solve a class of initial boundary value problems posed in a time-dependent convex domain for the sine-Gordon equation and for its linearized version. We give an explicit integral representation of the solution by using the Fokas transform method; this representation, which has an explicit exponential x and t dependence, is obtained by solving a d-bar problem in the complex plane. This d-bar ...

The paper is focused on numerical approximation of early exercise boundary within American put option pricing problem. Assuming non-dividend paying, American put option leads to two disjunctive regions, a continuation one and a stopping one, which are separated by an early exercise boundary. We present variational formulation of American option problem with special attention to early exercise a...

In cancer progress, the optical properties of tissues like absorption and scattering coefficient change, so by these changes, we can trace the progress of cancer, even it can be applied for pre-detection of cancer. In this paper, we investigate the effects of changes of optical properties on light penetrated into tissues. The diffusion equation is widely used to simulate light propagation into ...

In this paper, a Galerkin boundary node method (GBNM) is developed for boundary-only analysis of 2D problems in linear elasticity. The GBNM combines the variational form of a boundary integral formulation for the elastic equations with the moving least-squares approximations for generating the trial and test functions. Unlike the boundary node method, the main idea here is to use the Galerkin s...

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

Keywords: Rotating Navier–Stokes equations Exterior domain Boundary integral method Finite element approximation a b s t r a c t In this paper, we apply the boundary integral method to the linearized rotating Navier– Stokes equations in exterior domain. Introducing some open ball which decomposes the exterior domain into a finite domain and an infinite domain, we obtain a coupled problem by the...

This paper presents a boundary integral equation method with the adjoint generalized Neumann kernel for computing conformal mapping of unbounded multiply connected regions and its inverse onto several classes of canonical regions. For each canonical region, two integral equations are solved before one can approximate the boundary values of the mapping function. Cauchy's-type integrals are used ...