In this paper, a new collocation method, which is based on Boubaker polynomials, is introduced for the approximate solutions of a class of two-dimensional linear Fredholm integral equationsof the second kind. The properties of two-dimensional Boubaker functions are presented. The fundamental matrices of integration with the collocation points are utilized to reduce the solution of the integral ...

We consider the problem of nding a solution of a nonlinear system of equations subject to some box constraints. To this end, we introduce a new active set-type Newton method with global and local fast convergence properties. The method generates feasible iterates and has to solve only one linear system of equations at each iteration. Due to our active set strategy, this linear system is of redu...

Solving the incompressible Navier-Stokes equations for fluid flow using a semi-lagrangian method is a two step process [3]. In this paper we focus on the second step which involves the solution of a large sparse symmetric indefinite linear system of equations. Numerous numerical methods were used to solve this system. Here, the computation requirements of several are compared in hopes of findin...

We consider the problem of nding a solution of a nonlinear system of equations subject to some box constraints. To this end, we introduce a new active set-type Newton method with global and local fast convergence properties. The method generates feasible iterates and has to solve only one linear system of equations at each iteration. Due to our active set strategy, this linear system is of redu...

The objective of this study is to present a mathematical modeling and solution approach for the drying process of spheroidal solids with the application of microwave in capillary porous media based on the Luikov equations, composed of a system of linear and coupled partial differential equations arising from the energy, mass and pressure balances inside the solid matrix. Additionally, the power...

For strongly directed anisotropic processes such as coherence-enhancing di usion ltering it is crucial to use numerical schemes with highly accurate directional behavior. We show that this is not possible in a satisfactory way when discretizations are limited to 3 3 stencils. As a consequence, we investigate a novel algorithm based on 5 5 stencils. It utilizes recently discovered di erentiation...

This paper is concerned with the global asymptotic stability of the zero solution of the half-linear differential system x′ = − e(t)x+ f(t)φp∗(y) , y′ = − g(t)φp(x)− h(t)y , where p > 1, p∗ > 1 (1/p + 1/p∗ = 1), and φq(z) = |z|q−2z for q = p or q = p∗. The coefficients are not assumed to be positive. This system includes the linear differential system x′ = A(t)x with A(t) being a 2 × 2 matrix a...

In this paper we introduce a new procedure called α -Discounting Method for MultiCriteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty’s Analytical Hierarchy Process (AHP). It works for any number of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-...