123759806
Shooting Methods for Bifurcation Problems in Ordinary Differential Equations
We consider multiple shooting methods for bifurcation problems involving boundary value problems for ordinary differential equations. The case of bifurcation from a simple eigenvalue is treated as well as the solution of perturbed bifurcation problems. The original problem is discretizised via shooting techniques. This yields a finite-dimensional bifurcation problem which is solved by a special iteration scheme, having its origin in the theory of Lyapunov and Schmidt. A numerical example demonstrates that our algorithm workes well.
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.
7501088
Zur numerischen Behandlung gestörter Verzweigungsprobleme bei gewöhnlichen Differentialgleichungen
ZusammenfassungWir geben eine Möglichkeit der numerischen Behandlung von gestörten Verzweigungsproblemen bei Randwertaufgaben gewöhnlicher Differentialgleichungen mit Standardverfahren an. Dies gelingt mit Hilfe von Umparametrisierungen nach Störungsparametern und durch Aufstellung geeigneter regulärer Randwertaufgaben. Ein numerisches Beispiel — ein spezielles Stabknickungsproblem —belegt die Wirksamkeit unserer Methode.AbstractWe present a method for the numerical solution of perturbed bifurcation problems of boundary-value problems for ordinary differential equations by standard techniques. This is achieved by reparametrisation by perturbation parameters and definition of appropriate boundary-value problems which have isolated solutions. The efficiency of the method is demonstrated by a numerical example —a special rod buckling problem.
116988118
Efficient computation of stable bifurcating branches of nonlinear eigenvalue problems
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.
122551767
Numerical computation of the fourier transform using Laguerre functions and the Fast Fourier Transform
SummaryIn this paper we propose a numerical technique for the computation of Fourier transforms. It uses a bilateral expansion of the unknown transformed function with respect to Laguarre functions. The expansion coefficients are obtained via trigonometric interpolation and may be computed very efficiently by means of the Fast Fourier Transform. The convergence of the algorithm is analyzed and numerical results are presented which confirm that it works well.
107642364
The software factory challenge
The Eureka Software Factory project (ESF) was set up by a group of European partners in 1987. This text presents ESF's main ideas and achievements, and relates how the concepts pioneered by the project have become part of a general movement in both the the industrial and academic domains.
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.
16938020
EULER: a generalization of ALGOL and it formal definition: Part 1
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.