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...

In an aplanatic optical system, where the entrance pupil is not located at the front focal plane, a corresponding quadratic phase is expected at the back focal plane. However, tightly focused optical fields evaluated by methods based on the traditional Richards-Wolf approach, lacks this quadratic phase. In the current work we calculate the focused field, for both high and medium numerical apert...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...

Abstract. We give a surface integral derivation of the leading-order evolution equations for the spin and energy of a relativistic body interacting with other bodies in the post-Newtonian expansion scheme. The bodies can be arbitrarily shaped and can be strongly self-gravitating. The effects of all mass and current multipoles are taken into account. As part of the computation one of the 2PN pot...

We have developed a Green's function formalism to compute the local field distribution near an interface separating two media of different dielectric constants. The Maxwell's equations are converted into a surface integral equation ; thus it greatly simplifies the solutions and yields accurate results for interfaces of arbitrary shape. The integral equation is solved and the local field distrib...

this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.

A new technique is presented for accelerating the fast multipole method, allowing rapid solution of surface integral equations for wave scattering problems. A non-nested, ray propagation approach is used to compute a matrix-vector multiply in O(N 4=3) operations, where N is the number of unknowns in the discretized integral equation.

The surface integral formalism is used to derive the integral equations for the scattering of diffusive waves, which account for the contribution of object boundaries and interfaces between media and which are numerically solved without approximations. The extinction theorem and other surface integral theorems for diffusive waves are introduced to obtain the boundary values of both the photon d...