This paper gives a regular vector boundary integral equation for solving the problem of viscous scattering of a pressure wave by a rigid body. Firstly, single-layer viscous potentials and a generalized stress tensor are introduced. Correspondingly, generalized viscous double-layer potentials are defined. By representing the scattered field as a combination of a single-layer viscous potential an...

We present several coupled finite and boundary element formulations for the vibro-acoustic simulation of completely immersed bodies such as submarines. All formulations are based on the different use of standard boundary integral equations. In addition to the well known symmetric coupling we discuss two different approaches which are based on the weakly singular boundary integral equation only.

in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

A meshless method for the solution of 2D Helmholtz equation has been developed by using the Boundary Integral Equation (BIE) combined with Radial Basis Function (RBF) interpolations. BIE is applied by using the fundamental solution of the Helmholtz equation, therefore domain integrals are not encountered in the method. The method exploits the advantage of placing the source point always in the ...

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted,the density function is...

We consider a Fredholm integral equation of the second kind in L1([a, b],C), with a weakly singular kernel. Sufficient conditions are given for the existence and uniqueness of the solution. We adapt the product integration method proposed in C0([a, b],C) to apply it in L1([a, b],C), and discretize the equation. To improve the accuracy of the approximate solution, we use different iterative refi...

The approximate solution of a singular integral equation by Galerkin's method is studied. We discuss the theoretical aspects of such problems and give error bounds for the approximate solution.

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...

In this work we consider the numerical solution of a radiative transfer equation for modeling the emission of photons in stellar atmospheres. Mathematically, the problem is formulated in terms of a weakly singular Fredholm integral equation defined on a Banach space. Computational approaches to solve the problem are discussed, using direct and iterative strategies that are implemented in open s...