In this paper, we present higher order, single step Runge-Kutta type methods for solving parabolic equations. Details of second and third order methods are presented. The computational results for one second order process and two third order processes are presented and a comparison is made...

The rate of convergence of many sequences of numbers can be dramatically increased by non-linear sequence-to-sequence transformations. Several transformations of non scalar (vectorial or matricial) sequences are proposed in this paper. For a broad set of examples, their convergence accelerating...

Results in functional analysis are applied to the computation of the optimal control of a parabolic distributed parameter system. The control term is a coefficient of the state equation, and is computed by the steepest descent method. An a-priori feedback is determined in the case of a constant...

The following argument is presented:

The adaptive filtering and control problem for stochastic distributed systems involving space-dependent random parameters is treated using the partitioning/nonlinear separation approach. Both continuous-time and discrete-time models are considered.

Computer simulation of dynamic systems very often leads to the solution of a set of stiff ordinary differential equations. The solution of this set of equations involves the eigenvalues of its Jacobian matrix. The greater the spread in eigenvalues, the more time consuming the solutions become...

A physical modeling device and a computer graphic simulation program of the depletion of world energy reserve are developed to demonstrate how rapidly our energy reserve is depleted, how quickly and enormously our demands for energy grows, and how important energy conservation is to us. In both...

A higher order element, the Tocher 10 or C0 Cubic on triangles, is the base for formulation of a finite element algorithm for numerical calculation of fluid flows governed by the unsteady Navier-Stokes equations. Results from the calculation of supersonic free shear layer flow are numerically...

The concept of a quasi-parallel integration method is proposed as a potentially efficient way of handling the simulation of continuous systems that can be decomposed into a collection of loosely coupled sub-systems. Possible measures for evaluating the computational advantage of such an approach...

The author considers the use of the spectral equivalence property of operators for the study of the convergence of the hybrid iterative procedures. This procedure is realized in order to obtain a resolution of algebraic equations arising in the solution of boundary values problems for elliptic...