in this article the nonlinear mixed volterra-fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (m3d-bfs). this method converts the nonlinear mixed volterra-fredholm integral equations into a nonlinear system of algebraic equations. the illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.

We develop a numerical method based on Sine functions to obtain an approximate solution of a one-dimensional Cauchy singular integral equation (CSIE) over an arbitrary, smooth, open arc L of finite length in the complex plane. At the outset, we reduce the CSIE to a Fredholm integral equation of the second kind via a regularization procedure. We then obtain an approximate solution to the Fredhol...

PURPOSE In this study, we analyzed dielectric shimming by formulating it as an electromagnetic scattering problem using integral equations. METHODS Three-dimensional simulations of the radiofrequency field in two configurations using different materials were analyzed in terms of induced currents and secondary fields. A two-dimensional integral equation method with different backgrounds was us...

We consider an integral equation in the plane, in which the leading operator is of convolution type, and we prove that monotone (or stable) solutions are necessarily one-dimensional. Mathematics Subject Classification: 45A05, 47G10, 47B34.

The two-dimensional problem of advection–dispersion associated with a non-aqueousphase liquid (NAPL) pool is addressed using the boundary element method. The problem is appropriately posed with an inhomogeneous boundary condition taking into consideration the presence of the pool and the impermeable layer. We derive a Fredholm integral equation of the first kind for the concentration gradient a...