In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra  integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...

the asymmetric problem of rocking rotation of a circular rigid disk embedded in a finite depth of a transversely isotropic half-space is analytically addressed. the rigid disk is assumed to be in frictionless contact with the elastic half-space. by virtue of appropriate green's functions, the mixed boundary value problem is written as a dual integral equation. employing further mathematica...

In this paper, the evaluation of time profile of a femtosecond pulse laser propagated through biological tissues is studied. The majority of the biological tissues with a high scattering anisotropy must be considered as turbid media, that their optical responses are complicated. To study the propagation of ultra-short pulse in turbid media, the diffuse equation is used. In this study, the analy...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

Wave-equation migration velocity analysis (WEMVA) is an image-domain velocity model building technique based on band-limited wave propagation and designed especially for complex subsurface environments. It exploits the coherency of reflection events measured in extended images produced by a cross-correlation imaging condition with non-zero lags. Conventional approaches use either space-lags or ...

This paper is concerned with the existence of homoclinic orbits for secondorder differential equations with multiple lags. By using Mawhin’s continuation theorem, a nontrivial homoclinic orbit is obtained as a limit of a certain sequence of periodic solutions of the equation. AMS Subject Classifications: 34K15, 34C25.

By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form x (t) + cx (t− τ) = A (t, x(t)) x (t) + f (t, x (t− r1 (t)) , . . . , x (t− rk (t))) .

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...