12124100
EULER: a generalization of ALGOL, and its formal definition: Part II
In this section the algorithmic language EULER is described first informally and then formally by its syntax and semantics. An attempt has been made to generalize and extend some of the concepts of ALGOL, thus creating a language which is simpler and yet more flexible than ALGOL 60. A second objective in developing this language was to show that a useful programming language which can be processed with reasonable efficiency can be defined in rigorous formality.
814779
A microprogrammed implementation of EULER on IBM system/360 model 30
An experimental processing system for the algorithmic ~anguage EULER has been implemented in microprogramming on an IBM System/360 Model 30 using a second Read-Only Storage unit. The system consists of a mlcroprogrammed compiler and a microprogrammed String Language Interpreter, and of an I/O control program written in 360 machine language. The system is described and results are given in terms of microprogram and main storage space required and compiler and interpreter performance obtained. The role of microprogramming is stressed, which opens a new dimension in the processing of interpretive code. The structure and content of a higher level language can be matched by an appropriate interpretive language which can be executed efficiently by microprograms on existing computer hardware.
123856837
Numerische Behandlung von Verzweigungsproblemen bei Gewöhnlichen Randwertaufgaben
We consider the numerical solution of bifurcation problems for ordinary differential equations in the case of simple eigenvalues. First we treat the case of bifurcation from the trivial solution. We also give a new method for the numerical treatment of secondary bifurcation. It consists in the accurate determination of the bifurcation point for which a convex unrestricted minimization problem is derived, and the computation of both branches by conventional methods after transforming the problem.
123517753
On the numerical approximation of secondary bifurcation problems
We discuss stable numerical methods for the approximation of the solutions of a nonlinear parameter - dependent equation near a non-trivial bifurcation point. The problem of finding the bifurcation point is reformulated as a well-posed equation of higher dimension. The nearby branches can be calculated in a stable manner after applying a certain transformation having its origin in the Lyapunov — Schmidt theory. We also treat the perturbed bifurcation problem and present numerical results.
117077618
A Singular Multi-Grid Iteration Method for Bifurcation Problems
We propose an efficient technique for the numerical computation of bifurcating branches of solutions of large sparse systems of nonlinear, parameter-dependent equations. The algorithm consists of a nested iteration procedure employing a multi-grid method for singular problems. The basic iteration scheme is related to the Lyapounov-Schmidt method and is widely used for proving the existence of bifurcating solutions. We present numerical examples which confirm the efficiency of the algorithm.
120892864
Zur Verzweigung bei einfachen Eigenwerten
Let W and Y be real Banach spaces and F:W → Y be a smooth mapping. Let xɛW be a solution of F(z)=0, Bifurcation theory deals with the problem of determining the structure of the zeros of F near x. We give a modification of a well-known theorem of Crandall and Rabinowitz which is useful for applications, i.e. for the computation of bifurcation points. A numerical example is included.
117989535
Numerical Methods for Bifurcation Problems — A Survey and Classification
The purpose of this paper is to give an account of recent developments in numerical methods for the solution of bifurcation problems. For readers not too familiar with our subject we shall first summarize important applications of bifurcation and dicuss some of the basic ideas, problems and tools of bifurcation theory.