Consider solving the Dirichlet problem Au(P) = o, Pem2\s, u(P) = h(P), Pes, sup \u(P)\ < CO, Pes2 with S a smooth open curve in the plane. We use single-layer potentials to construct a solution u(P). This leads to the solution of equations of the form j g(Q)\og\P-Q\dS(Q) = h(P), PeS. This equation is reformulated using a special change of variable, leading to a new first-kind equation with a sm...

We propose a discrete collocation method for the boundary integral equations which arise from solving Laplace's equation u = 0. The Laplace's equation is deened on connected regions D in R 3 with a smooth boundary S. The piecewise polynomial interpolation in the parametrization variables along with the collocation method is used, and a numerical integration scheme for collocation integrals is g...

in this paper, we introduce an efficient method based on haar wavelet to approximate a solutionfor the two-dimensional linear stochastic fredholm integral equation. we also give an example to demonstrate the accuracy of the method.

In this paper, we establish some results for a Volterra–Hammerstein integral equation with modified arguments: existence and uniqueness, inequalities, monotony Ulam-Hyers-Rassias stability. We emphasize that many problems from the domain of symmetry are modeled by differential equations those approached in stability point view. literature, Fredholm, Volterra Hammerstein integrals symmetric kern...

This study is devoted to solve the Chandrasekhar integral equation that it used for modeling problems in theory of radiative transfer a plane-parallel atmosphere, and others research areas like kinetic gases, neutron transport, traffic model, queuing among others. First all, we transform into nonlinear Hammerstein-type with corresponding Nemystkii operator proper nonseparable kernel. Them, appr...

In this paper, a new simple direct method to solve nonlinear Fredholm-Volterra integral equations is presented. By using Block-pulse (BP) functions, their operational matrices and Taylor expansion a nonlinear Fredholm-Volterra integral equation converts to a nonlinear system. Some numerical examples illustrate accuracy and reliability of our solutions. Also, effect of noise shows our solutions ...