Limit boundary value problems in regions with random fine grained boundaries

Neural-network methods for boundary value problems with irregular boundaries

Partial differential equations (PDEs) with boundary conditions (Dirichlet or Neumann) defined on boundaries with simple geometry have been successfully treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a r...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Limit Theorems for Random Walks with Boundaries

In this review, we consider boundary problems for random walks generated by sums of independent items and some of their generalizations. Let 1, 42, . . * be identically distributed independent random variables with distribution frunction F(x). Let S = 0, Sn = Sk= Ok with n = 1, 2, * -. We shall study the properties of the random trajectory formed by the sums S0, S1, 82, . Let n be an integer pa...

Random Walks for Solving Boundary-Value Problems with Flux Conditions

We consider boundary-value problems for elliptic equations with constant coefficients and apply Monte Carlo methods to solving these equations. To take into account boundary conditions involving solution’s normal derivative, we apply the new mean-value relation written down at boundary point. This integral relation is exact and provides a possibility to get rid of the bias caused by usually use...

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.