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We introduce a new system of surface integral equations for Maxwell’s transmission problem in three dimensions (3-D). This system has two remarkable features, both of which we prove. First, it is well-posed at all frequencies. Second, the ...

In the present study, we construct a considerably fast convergent multistep collocation technique in order to solve Volterra integral equations, especially first-kind ones with variable vanishing delays. Through a robust theoretical analysis, the ...

In the current study, we deal with a linear system of integral-algebraic-equations (IAEs) with vanishing delay arguments, which can be considered as the most momentous novelty of this work, since it is the first time where these two concepts have ...

In this paper, we develop Galerkin’s residual-based numerical scheme for solving a system of Cauchy-type singular integral equations of index minus N using Chebyshev polynomials of the first and second kind, where N is the total number of Cauchy-...

• A residual based Galerkin’s method using Chebyshev polynomials has been developed.
• A system of Cauchy singular integral equations (SCSIE) has been numerically solved.
• The well-posedness of the SCSIE has been shown using the ...

We study a non-local optimal control problem involving a linear, bond-based peridynamics model. In addition to existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter $\delta$, which controls the ...$$

The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of two-dimensional scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary ...

The half-space matching (HSM) method has recently been developed as a new method for the solution of two-dimensional scattering problems with complex backgrounds, providing an alternative to perfectly matched layers or other artificial boundary ...

In this paper, we consider product integration method based on orthogonal polynomials to solve mixed system of Volterra integral equations of the first and second kind with weakly singular kernels. For investigation of the theoretical and ...

We present a new integral representation for the unsteady, incompressible Stokes or Navier--Stokes equations, based on a linear combination of heat and harmonic potentials. For velocity boundary conditions, this leads to a coupled system of integral equations:...

In this paper, the problem of finding numerical solution for a system of Cauchy type singular integral equations of first kind with index zero is considered. The analytic solution of such system is known. But it is of limited use as it is a nontrivial ...

Based on Jacobi polynomials, an operational method is proposed to solve the generalized Abels integral equations (a class of singular integral equations). These equations appear in various fields of science such as physics, astrophysics, solid mechanics,...

The Legendre spectral Tau matrix formulation is proposed to approximate solution of singular system of Volterra integro-differential equations. The existence and uniqueness solution of this system are investigated by means of the ź -smoothing property ...

This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three different systems of boundary integral equations via direct and indirect approaches. Existence ...

The ź-smoothing property of a one-dimensional Volterra integral operator and some projectors (Liang and Brumer, SIAM J. Numer. Anal. 51, 2238---2259 (2013)) are extended for two-dimensional integral-algebraic equations (TIAEs). Using these concepts, we ...

We present a high performance computing framework for quantifying uncertainties in the propagation of acoustic waves through a stochastic media comprising a large number of three-dimensional particles. We subsequently describe an efficient postprocessing ...

This paper deals with some theoretical and numerical results for Volterra Integral Algebraic Equations (IAEs) of index-1 with weakly singular kernels. This type of equations typically has solutions whose derivatives are unbounded at the left endpoint of ...

A significative number of recent applications require numerical solution of large systems of Abel-Volterra integral equations. Here we propose a parallel algorithm to numerically solve a class of these systems, designed for a distributed-memory MIMD ...

Here we present a fully discretized projection method with Fourier series which is based on a modification of the fast Fourier transform. The method is applied to systems of integro-differential equations with the Cauchy kernel, boundary integral ...