in this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the laplacian equation. themethod is based on the use of the galerkin method with cas wavelets constructed on the unit interval as basis.this approach utilizes the non-uniform gauss-legendre quadrature rule for ...

Alternative Legendre polynomials (ALPs) are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given an...

In this paper, Adomian decomposition method (ADM) and homotopy analysis method (HAM) are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind(FV FIE− 2). we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this s...

Some existence and uniqueness theorems are established for weakly singular Volterra and Fredholm-Volterra integral equations in C[a, b]. Our method is based on fixed point theorems which are applied to the iterated operator and we apply the fiber Picard operator theorem to establish differentiability with respect to parameter. This method can be applied only for linear equations because otherwi...

In this paper, an iterative scheme for extracting approximate solutions of two dimensional Volterra-Fredholm integral equations is proposed. Considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. Several examples are provided to demonstrate the effi...

in this paper, we present a new computational technique for solving nonlinear fredholm integral equations of the second kind. this proposed method is based on galerkin method and is computationally very attractive. moreover, for reducing the operations in comparing similar works, we design our algorithm based on transformations of orthogonal polynomials in approximation coefficients calculating...

We characterize the optimal signal-adaptive liquidation strategy for an agent subject to power-law resilience and zero temporary price impact with a Gaussian signal, which can include e.g OU process or fractional Brownian motion. show that selling speed ut? is Volterra of form u?(t)=u0(t)+u¯(t)+?0tk(u,t)dWu on [0,T), where k(?,?) u¯ satisfy family (linear) Fredholm integral equations first kind...

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...