Hybrid computer solution of PDE's using Laplace-modified Galerkin approximation

A method for the hybrid computer solution of a large class of P.D.E.'s, using a Laplace-modified Galerkin approximation, is presented. Hybrid implementation of the proposed method is discussed in detail. Using this method, a number of linear and nonlinear problems are solved. The hybrid solution is compared with the exact and/or all digital solutions and features such as accuracy, efficiency, generality, and ease of use are discussed. It is concluded that the proposed method is quite viable.     

Solving parabolic PDE's by a decomposition method

The paper deals with the application of the hybrid method of decomposition for the solution of two-dimensional parabolic partial differential equations with constant coefficients. The convergence and accuracy of the CSDT method are analysed, deriving the form of the relationship between ‘eigenvalues’ and the time step. Theoretical problems of this method of decomposition are mentioned. Also, the expression for computing the coefficients for various types of boundary problems has been derived. Practical applications of the method are presented. The cubic spline function interpolation is used for the continuous signal reproduction in the hybrid system. Some results obtained are presented at the end.     

The EDP auditor's role in computer security

EDP auditors are playing an increasingly crucial role in the computer security process. They are a new type of technical specialists. They work at the point where management of computing and the achievement of traditional auditing objectives converge. However, they use methods different from those long employed by conventional auditors. EDP auditors basically assure that management effectively controls the way in which computing is done and that records related to that data processing are current and accurate. However, they do not seek, primarily, to find fraud.     

An integral equation method for the numerical solution of Laplace's equation without Green's function

The common way to establish an integral equation for the solution of Laplace's equation uses the Green's function of the given equation. It will be shown in this paper that an integral equation can also be constructed by using a particular solution of the Laplace equation as the Kernel of the integral equation.     

The direct solution of periodic parabolic problems by boundary-value techniques

In this paper fast direct methods are presented for the solution of the parabolic boundary value problem. The algorithms used are block variants of the cyclic factorisation algorithm previously presented in Evans [1]     

Johnson's method of optimum design applied to a problem with simple functional relationships

This paper illustrates the use of a well-proven but little known method of optimization for mechanical design problems. The method, developed by R. C. Johnson, is applied to a previously formulated problem which has been solved by other techniques. Solution by Johnson's method reveals important facets of the problem which are not made evident in other methods of solution. The effects of modified constraint conditions can be rapidly determined using an interactive computer program based on the flowchart presented.     

Stable iterative hybrid method for the solution of weak nonlinear parabolic differential equations

In the hybrid computer solution of a parabolic differential equation the equation may be approximated by a set of coupled ordinary differential equations, one equation for each spatial station. The set is integrated by the analog computer one equation (or one group of equations) at a time in a serial fashion using a relaxation technique and employing the digital computer for function storage and playback. By using the iterative time-sharing computation of this class of equations the authors have received new general results.     

Children's questions: A study of questions children ask while learning to use a computer

This paper reports the results of a study conducted at a Texas elementary school which examined the types of questions children ask as they learn to use a computer. Throughout the study, a log was kept of each child's questions. Questions were then classified into eight distinct categories. Results indicate that children asked the most questions about the keyboard, how to enter data and the meaning of program instructions. Children also had difficulty remembering operating system commands and had problems distinguishing characters on the screen. Elaboration of the classification scheme to other populations should add to the general knowledge of human-computer interface and should help improve the understanding of the questioning process.     

Numerical solution of parabolic,second-order differential equations on a computer with parallel computations

Cybernetics and Systems Analysis -     

Practical applications of an integral equation method for the solution of Laplace's equation

An integral equation method for the solution of Laplace's equation, originally proposed for boundary value problems in a single medium, is here extended to problems involving multiple media. The extended method has been used to compute the internal thermal resistance of electric cables and some numerical results are presented.     

Numerical solution of Laplace's equation as an integral equation of the first kind

A Fourier approximation method is developed for the simple layer potential reformulation of Laplace's equation. The efficacy of the method is demonstrated in computational examples, and also analyzed theoretically.