In terms of observational data, there are some problems in the standard Big Bang cosmological model. Inflation era, early accelerated phase of the evolution of the universe, can successfully solve these problems. The inflation epoch can be explained by scalar inflaton field. The evolution of this field is presented by a non-linear differential equation. This equation is considered in FLRW model...

A solution for a class of two-dimensional elasticity problems concerning an isotropic body with an arc crack in its interior is obtained in terms of an integral taken around the exterior boundary of the body. A numerical procedure for solving this integral equation is outlined and numerical results for a test problem are given.

In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...

The three-dimensional electrostatic field configuration in gas ionization detectors has been simulated using an efficient and precise nearly exact boundary element method (NEBEM) solver set up to solve an integral equation of the first kind. This recently proposed formulation of BEM and the resulting solver use exact analytic integral of Green function to compute the electrostatic potential for...

Questions of solution of three-dimensional diffraction problems are considered. Each problem is formulated as a single weakly-singular integral equation of the 1st kind for a single unknown function. Discretization of these equations is realized by means of special smoothing method of integral operators kernels. Numerical solutions of systems of linear algebraic equations, approximating integra...

In this paper, an efficient method is presented for solving two dimensional Fredholm and Volterra integral equations of the second kind. Chebyshev polynomials are applied to approximate a solution for these integral equations. This method transforms the integral equation to algebraic equations with unknown Chebyshev coefficients. The high accuracy of this method is verified through some numeric...

Integral equation methods have been used with great success in electromagnetic scattering calculations and in other problems involving unbounded computational domains. Their application is in many cases limited by the storage requirements of dense matrices and also by the rapidly increasing computational time. However, the use of iterative solvers and special methods for computing the matrix-ve...

This study presents a Feynman-Kac path-integral implementation for solving the Dirichlet problem for Poisson’s equation. The algorithm is a modified “walk on spheres” (WOS) that includes the FeynmanKac path-integral contribution for the source term. In our approach, we use the Poisson kernel instead of simulating Brownian trajectories in detail to implement the path-integral computation. We der...