We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...

This paper describes the characteristics of small-amplitude waves generated by a sinusoidally oscillating, inclined paddle-type wavemaker operating in a constant-depth channel. Two-dimensional, linearized potential flow is assumed. A semi-analytical method, the boundary collocation method, is used to establish the relationship between wave amplitude and paddle stroke. The numerical results are ...

Spurious eigensolutions in the boundary integral equation (BIE) or boundary element method (BEM) for doublyconnected domain problems, the eccentric and annular membranes, are studied analytically and numerically in this paper. For the mathematical analysis, we employ the null-field integral equation, the degenerate kernels and the Fourier series to prove the existence of spurious eigensolutions...

The weak-form of Helmholtz differential equation, in conjunction with vector test-functions (which are gradients of the fundamental solutions to the Helmholtz differential equation in free space) is utilized as the basis in order to directly derive non-hyper-singular boundary integral equations for the velocity potential, as well as its gradients. Thereby, the presently proposed boundary integr...

In this paper, the evaluation of time profile of a femtosecond pulse laser propagated through biological tissues is studied. The majority of the biological tissues with a high scattering anisotropy must be considered as turbid media, that their optical responses are complicated. To study the propagation of ultra-short pulse in turbid media, the diffuse equation is used. In this study, the analy...

Abstrac-Based on a variational principle, a new approach to derive the exact boundary equation for the analysis of nonlinear Reissner plates and a related existing criterion for the solution of the boundary integral equation is presented in this paper. In this procedure, the boundary and the domain of the plate are discredited to solve the nonlinear problems. All unknown variables are at the bo...

Time-dependent problems that are modeled by initial-boundary value problems for parabolic or hyperbolic partial differential equations can be treated with the boundary integral equation method. The ideal situation is when the right-hand side in the partial differential equation and the initial conditions vanish, the data are given only on the boundary of the domain, the equation has constant co...

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The...

We develop a simple, efficient numerical method of boundary integral type for solving an elliptic partial differential equation in a three-dimensional region using the classical formulation of potential theory. Accurate values can be found near the boundary using special corrections to a standard quadrature. We treat the Dirichlet problem for a harmonic function with a prescribed boundary value...