Although scientific computing traditionally involves numerical data, the need for symbolic representation is now recognized. In this context, we have developed a knowledge-based system coupled with a finite element library. It guides the user in the specification of the physical problem, finds a...

The Korteweg-de Vries equation is numerically solved by using a new algorithm based on the quintic spline approximation. An iterative scheme having O(k2 + kh2) accuracy and five-band constant coefficients system of equations is devised. The stability of the proposed scheme is discussed....

Proportional plus integral plus derivative (PID) control is a well established technique for industrial control and possesses a high flexibility for use in many applications. However the tuning procedure is in many situations nontrivial, which implies that it is difficult to find the values of...

In this paper implementations of three numerical schemes for the numerical simulation of the complex modified Korteweg-de Vries (CMKdV) equation are reported. The first is an integrable scheme derived by methods related to the Inverse Scattering Transform (IST). The second is derived from the...

This note deals with a simulation algorithm for a reheating process of long steel products. In the steel industry, it is not always possible to measure the temperature of slabs during the reheating process. Therefore the well-known two-dimensional model of heat conduction with mixed...

A new grid-free method for approximating incompressible thermal boundary layers is introduced. The computational elements are segments of vortex sheets which are heated. The method solves the general Prandtl boundary layer equations. More efficient methods of treating the diffusion and source...

Variational inequality theory provides us with a general and unified framework to study a large class of unrelated free and moving boundary problems that arise in pure and applied sciences. In this paper we show that a class of variational inequalities related with obstacle problems can be...

Kinematics of surfaces in 3-dimensional space is formulated in terms of the differential geometry. The formulation is intrinsic and the surface is described by its metric and curvature tensors. It is found that the introduction of nontrivial time evolution of coordinate system makes the theory...

Based on singular perturbation analysis of nonlinear PDEs, we can get an approximate solution of the equation, constructed from a solution of the reduced equation associated with the given nonlinear PDE, and correction terms corresponding to boundary layers and interior layers. By applying the...