Abstract: In this paper, we explore the applicability of the Sinc-
Collocation method to a three-dimensional (3D) oceanography model.
The model describes a wind-driven current with depth-dependent
eddy viscosity in the complex-velocity system. In general, the
Sinc-based methods excel over other traditional numerical methods
due to their exponentially decaying errors, rapid convergence and
handling problems in the presence of singularities in end-points.
Together with these advantages, the Sinc-Collocation approach that
we utilize exploits first derivative interpolation, whose integration
is much less sensitive to numerical errors. We bring up several
model problems to prove the accuracy, stability, and computational
efficiency of the method. The approximate solutions determined by
the Sinc-Collocation technique are compared to exact solutions and
those obtained by the Sinc-Galerkin approach in earlier studies. Our
findings indicate that the Sinc-Collocation method outperforms other
Sinc-based methods in past studies.
Abstract: In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To
this purpose, we consider two stages of approximation.
First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems
and optimal control problems. Finally numerical examples is
proposed.
Abstract: The goal of this paper is to find Wardrop equilibrium
in transport networks at case of uncertainty situations, where the
uncertainty comes from lack of information. We use simulation tool
to find the equilibrium, which gives only approximate solution, but
this is sufficient for large networks as well. In order to take the
uncertainty into account we have developed an interval-based
procedure for finding the paths with minimal cost using the
Dempster-Shafer theory. Furthermore we have investigated the users-
behaviors using game theory approach, because their path choices
influence the costs of the other users- paths.
Abstract: The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.
Abstract: In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.
Abstract: In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.