In this paper, Bezier surface form is used to find the approximate solution of delay differential equations (DDE’s). By using a recurrence relation and the traditional least square minimization method, the best control points of residual function can be found where those control points determine the approximate solution of DDE. Some examples are given to show efficiency of the proposed method.

It presents and analyzes the Euler methods for stochastic age-dependent population equations driven by Poisson random jump measure; Under the Local Lipschitz condition, we prove that the Euler approximation solution converges to the exact solution in the mean-square sense. An example is given to illustrates our results.

Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root of the viscosity. Unlike previous results on LDP for hydrodynamical models, the weak convergence is proven by tightness properties of the distribution of the solution in appropriate functional spaces.

A factoring and block elimination method for the fast numerical solution of block five diagonal linear algebraic equations is described. Applications of the method are given for the numerical solution of several boundary-value problems involving the biharmonic operator. In particular, 22 eigenvalues and eigenfunctions of the clamped square plate are computed and sketched.

Let us now consider the case where the solution is overdetermined. Now there are more sets of equations than there are unknowns, which is manifested by A being rectangular, with more rows than columns (i.e. tall and thin). In general, there will be no vector x that satisfies all of the equations. In the absence of a perfect solution, we aim to find a solution that minimizes the square error bet...

An alternating direction implicit (ADI) three-dimensional fluid parabolic equation solution method with enhanced accuracy is presented. The method uses a square-root Helmholtz operator splitting algorithm that retains cross-multiplied operator terms that have been previously neglected. With these higher-order cross terms, the valid angular range of the parabolic equation solution is improved. T...

GMRES is a popular iterative method for the solution of large linear systems of equations with a square nonsingular matrix. When the matrix is singular, GMRES may break down before an acceptable approximate solution has been determined. This paper discusses properties of GMRES solutions at breakdown and presents a modification of GMRES to overcome the breakdown.

In this work we derive the structural properties of the Collocation coefficient matrix associated with the Dirichlet-Neumann map for Laplace’s equation on a square domain. The analysis is independent of the choice of basis functions and includes the case involving the same type of boundary conditions on all sides, as well as the case where different boundary conditions are used on each side of ...

The effects of natural convection with and without the interaction of surface radiation in square and rectangular enclosures have been studied, numerically and theoretically. The analyses were carried out over a wide range of enclosure aspect ratios ranging from 0.0625 to 16, including square enclosures in sizes from 40cm to 240cm, with cold wall temperatures ranging from 283 to 373 K, and hot ...

The collision of a quantum Gaussian wave packet with a square barrier is solved explicitly in terms of known functions. The obtained formula is suitable for performing fast calculations or asymptotic analysis. It also provides physical insight since the description of different regimes and collision phenomena typically requires only some of the terms. PACS numbers: 03.65.-w Gaussian wave packet...