Nekrasov's integral equation describing water waves of permanent form, determines the angle φ (s) that the wave surface makes with the horizontal. The independent variable s is a suitably scaled velocity potential, evaluated at the free surface, with the origin corresponding to the crest of the wave. For all waves, except for amplitudes near the maximum, φ (s) satisfies the inequality |φ (s) | ...

A new higher-order method of moment (MoM) technique is presented for volume-surface integral equations (VSIE) for electromagnetic modeling of composite metallic and dielectric objects. The higher-order MoM scheme comprises higher-order hierarchical Legendre basis functions and an accurate representation of the object by higher-order curvilinear elements. Due to the orthogonal nature of the basi...

In this paper we are concerned with the numerical analysis of the collocation method based on graded meshes of second kind integral equations on the real line of the form φ(s)=ψ(s)+ ∫ R κ(s − t)z(t)φ(t) dt, s ∈R, where κ ∈ L1(R), z ∈ L∞(R), and ψ ∈ BC(R), the space of bounded continuous complex-valued functions on R, are assumed known and the function φ ∈ BC(R) is to be determined. We introduce...

‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...

in this paper, a generalized method for accurate full-wave analysis of shielded mic's and the three-layer microstrip structure enclosed in a rectangular cavity based on mixed potential integral equation (mpie) derived in real space have been developed. method of moments (mom) with galerkin technique has been used for the solution of the integral equation to obtain the surface electric currents ...

[This document is http://www.math.umn.edu/ ̃garrett/m/complex/notes 2014-15/09c Riemann and zeta.pdf] 1. Riemann’s explicit formula 2. Analytic continuation and functional equation of ζ(s) 3. Appendix: Perron identity [Riemann 1859] exhibited a precise relationship between primes and zeros of ζ(s). A similar idea applies to any zeta or L-function with analytic continuation, functional equation, ...

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

We study a boundary integral equation method for solving Laplace s equation u with nonlinear boundary conditions This nonlinear boundary value problem is reformulated as a nonlinear boundary in tegral equation with u on the boundary as the solution being sought The integral equation is solved numerically by using the collocation method with piecewise quadratic functions used as approximations t...