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...

Effective anti-plane quasistatic moduli for 2D piezoelectric phononic crystals of arbitrary anisotropy are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in one dimension with direct numerical integration along the other direction. As a result, the MM method converges much qui...

Performances of iterative blind deconvolution methods for motion-blurred images are usually reduced depending on the accuracy of the required initial guess of the blur. We examine this dependency, and a two-stage restoration procedure is proposed: First we perform a direct technique with a single straight-forward process to produce a rough initial estimate of the blur, and then an iterative tec...

introduction: due to irregular growth and expansion of cities, especially in developing countries, various issues and difficulties have arisen in different economic, social and ecological fields and various measurements and approaches in order to supply desirable conditions for today and future generations. healthy city approach is one these approaches as today it’s a new mechanism proposed by ...

we reduce the two phase stefan problem with kinetic to a system of nonlinear volterra integral equations of second kind and apply newton's method to linearize it. we found product integration solution of the linear form. sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.