In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

in this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. but we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as legendre ...

The nonlinear integral equation P (x) = ∫ β α dy w(y)P (y)P (x + y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P (x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial sol...

The standard approach to calculating electrostatic forces and ca-pacitances involves solving a surface integral equation of the rst kind. However, discretizations of this problem lead to ill-conditioned linear systems and second-kind integral equations usually solve for the dipole density, which can not be directly related to electrostatic forces. This paper describes a second-kind equation for...

1 Prliminaries 2 1.1 Basic Probability concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Stochastic Differential Equations (SDE’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Langevin equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Ito integral and basics of Ito calculus . . . . . . . . . . . . . . ....