The elasticity mixed boundary values problems dealing with half-space contact are generally well resolved. A large number of these solutions are obtained by using the integral transformation method and methods based the integral equations. However, the problems of finite layer thicknesses are less investigated, despite their practical interests. This study resolves a quasi-stationary problem of...

We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly known joint probability distribution of the extremal processes. We also delineate circumstances under which the value of a stopping problem induces directly this...

Richardson extrapolation is applied to improve the accuracy of the numerical solution of boundary integral equations. The boundary integral equations arise from a direct boundary integral method for solving a Laplace’s equation interior Dirichlet problem. Specifically, the Richardson extrapolation is used to improve the accuracy of collocation. Numerical justification is provided to support the...

An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are u...

A novel iteration scheme, using boundary integral equations, is developed for error estimation in the boundary element method. The iteration scheme consists of using the boundary integral equation for solving the boundary value problem and iterating this solution with the hypersingular boundary integral equation to obtain a new solution. The hypersingular residual r is consistently defined as t...

This paper studies a nonlinear fractional differential equation of an arbitrary order with four-point nonlocal integral boundary conditions. Some existence results are obtained by applying standard fixed point theorems and Leray-Schauder degree theory. The involvement of nonlocal parameters in four-point integral boundary conditions of the problem makes the present work distinguished from the a...

We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly known joint probability distribution of the extremal processes. We also delineate circumstances under which the value of a stopping problem induces directly this...

a method has been presented for finding the solution surface of the npde: u  c , bounded by a general space curve. the method is based on the geometric characteristics of the surface, and is called the “cone-slot method”. it has been shown that such a surface can be obtained by movement of a cone inside the slot formed by the boundary space curve. an algorithm has been suggested on the basis ...

This paper studies a boundary value problem of nonlinear fractional differential equations of order q ∈ 1, 2 with three-point integral boundary conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Our results are new in the sense that the nonlocal parameter in three-point integral boundary conditions appears ...