In this study a numerical method is developed to solve the Hammerstein integral equations. To this end the kernel has been approximated using the leastsquares approximation schemes based on Legender-Bernstein basis. The Legender polynomials are orthogonal and these properties improve the accuracy of the approximations. Also the nonlinear unknown function has been approximated by using the Berns...

In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...

Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...

‎in this paper‎, ‎an approach based on statistical spline model (ssm) and collocation method is proposed to solve volterra-fredholm integral equations‎. ‎the set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials‎. ‎under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎numerical results on some problems are given...

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...

this paper is concerned with a technique for solving volterra integral equations in the reproducing kernel hilbert space. in contrast with the conventional reproducing kernel method, the gram-schmidt process is omitted here and satisfactory results are obtained.the analytical solution is represented in the form of series.an iterative method is given to obtain the approximate solution.the conver...

The dual boundary element method is formulated for the analysis of linear elastic cracked plates. The dual boundary integral equations of the method are the displacement and the traction equations. When these equations are simultaneously applied along the crack boundaries, general crack problems can be solved in a single-region formulation, with both crack boundaries discretized with discontinu...

The objective of this work is to develop deep theoretical methods that are based on the solution of the integral boundary layer equations for investigating film cooling in liquid rocket engine. The integral model assumes that heat is transferred from hot free stream gas to the liquid film both by convection and radiation. The mass is transferred to the free srteam gas by the well-known blowing ...