in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

Due to the importance effect of magnetic field on the history of long-term radial and circumfer-ential creep strain and radial displacement for a three-phase nano-composite exposed to an internal pressure and placed uniform temperature, the present article subject has been pro-posed. Three-phase nano-composite made of single-walled carbon nano tubes (SWCNTs)/ glass fiber (GF)/vinylester used to...

In the present study, the magnetic field effects of the elastic response of the polymeric piezoelectric cylinder reinforced with the carbon nanotubes (CNTs) are studied. The cylinder is subjected to an internal pressure, a constant electric potential difference at the inner and outer surfaces, and the thermal and magnetic fields. The Mori-Tanaka model is used for obtaining the equivalent materi...

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...

The dynamics of an interface between the normal and superconducting phases under nonstationary external conditions is studied within the framework of the time-dependent Ginzburg-Landau equations of superconductivity, modified to include thermal fluctuations. An equation of motion for the interface is derived in two steps. First, the method of matched asymptotic expansions is used to derive a di...

In this study an analytical method is developed to obtain the response of electro-magneto-thermo-elastic stress and perturbation of a magnetic field vector for a thick-walled spherical functionally graded piezoelectric material (FGPM). The hollow sphere, which is placed in a uniform magnetic field, is subjected to a temperature gradient, inner and outer pressures and a constant electric potenti...

in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.

We deal with the scattering phenomenon from an abruptly terminated asymmetrical slab waveguide for the case of transverse magnetic (TM) modes. The analysis uses both the integral equation method and the variational technique. The reflection coefficient of the dominant TM guided mode and the far-field radiation pattern are computed, and the discontinuity of the electric field distribution on the...

We investigate the topological quenching of spin tunneling in Mn12-acetate molecules with an applied magnetic field along the hard axis. The model Hamiltonian describing this system has a fourth-order term due to the tetragonal anisotroy. We treat this model using the discrete phase integral formalism in which the Schrödinger equation corresponding to the Hamiltonian becomes a nine-term recursi...

in this paper, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...