The traffic flow within a section of roadway can be described by an integro-differential equation dependent on the traffic concentration. Using theBanach fixed point theorem it is shown that there exists a unique solu...
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The traffic flow within a section of roadway can be described by an integro-differential equation dependent on the traffic concentration. Using theBanach fixed point theorem it is shown that there exists a unique solution of that equation between definite limits and how it can be found. There is no essential loss of generality at the functions of the model. The numerical results are discussed.
A generalization of the concept of a divided difference operator introduced by J. W. Schmidt is derived. The inclusion of solutions by certain Regula-falsi-methods realized by a well known approximation of the Jacobia...
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A generalization of the concept of a divided difference operator introduced by J. W. Schmidt is derived. The inclusion of solutions by certain Regula-falsi-methods realized by a well known approximation of the Jacobian matrix, which is no divided difference operator in the sense of Schmidt but a realization of this generalization, is proved.
Interval arithmetic was introduced by R. E. Moore in [1966]. It helps to get bounds for the range of function. Sometimes—but not always—these bounds overestimate the range, sometimes they are even extremely pessimis...
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Interval arithmetic was introduced by R. E. Moore in [1966]. It helps to get bounds for the range of function. Sometimes—but not always—these bounds overestimate the range, sometimes they are even extremely pessimistic. In what follows the reasons for this behaveour will be shown. Furthermore criteria are developed which show if a function is “optimal”, i. e. not overestimating the range. An appl.cation of this theory to linear systems of equations is given. It produces classes of matrices and of righthand sides for which the Gauss elimination method has this optimality.
The results of the theory of linear automata which concern the reduction, the cycle lenghts of the autonomous factor, and the isomorphism between the autonomous and other factors of the automata are generalized to the...
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The results of the theory of linear automata which concern the reduction, the cycle lenghts of the autonomous factor, and the isomorphism between the autonomous and other factors of the automata are generalized to the quasilinear automata. As the linear automat gives rise to introduce the cylic codes, so the quasi cylic to a corresponding class of codes.
It is presented an errorestimation with regard to a partial order for a solutionx* of a nonlinear system of equationsf(x)=0. Its development also allows a statement about the unambiguity of the *** results are appl.ed...
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It is presented an errorestimation with regard to a partial order for a solutionx* of a nonlinear system of equationsf(x)=0. Its development also allows a statement about the unambiguity of the *** results are appl.ed to a system of difference equations and to an algebraic Eigenvalueproblem.
In the present paper a new predictor-corrector-method with an exponentially fitted version is given for the numerical treatment of the initial value problems for systems of first oder differential equations. For a cla...
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In the present paper a new predictor-corrector-method with an exponentially fitted version is given for the numerical treatment of the initial value problems for systems of first oder differential equations. For a class of linear differential equations the exact solution is obtained. Some numerical examples show the appl.cation of the new multistep algorithms.
The nature of triplex numbers, and the necessity, to insert these into a high-level programming language, are outlined. The insertion of the typtriplex into ALGOL 60 leads to the languageTriplex-ALGOL. The syntax of t...
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The nature of triplex numbers, and the necessity, to insert these into a high-level programming language, are outlined. The insertion of the typtriplex into ALGOL 60 leads to the languageTriplex-ALGOL. The syntax of this language is specified and its semantic is described in detail.
The result of this paper is the economizing of cpu-time by identical guaranteed precision of the approximate solution. This is possible by an optimal selection ofn j in every iteration stepj, wheren j is the number of...
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The result of this paper is the economizing of cpu-time by identical guaranteed precision of the approximate solution. This is possible by an optimal selection ofn j in every iteration stepj, wheren j is the number of subintervals for the numerical integration. The determination ofn1,n2, ... is reduced to the solution of a solvable convex optimization job.
An interpolation on equidistant points of an infinite interval in form of an infinite series is investigated, which is closely related to the trigonometric interpolation. Under considerably weak conditions on the beha...
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An interpolation on equidistant points of an infinite interval in form of an infinite series is investigated, which is closely related to the trigonometric interpolation. Under considerably weak conditions on the behaviour at infinity a remainder for the interpolation of functions holomorphic in a strip parallel to the real axis of the complex plane is given, from which follows that the error of interpolation converges exponentially and uniformly to zero, as the step size tends to zero. Differentiating, and integrating the interpolation series, formulas of numerical differentiation and integration of improper integrals are obtained.
The classical transportation problem is augmented by a set of additional constraints, which are arbitrary linear equalities or inequalities and may contain also some additional variables. A special algorithm for this ...
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The classical transportation problem is augmented by a set of additional constraints, which are arbitrary linear equalities or inequalities and may contain also some additional variables. A special algorithm for this linear program is described. The method is thought to be efficient, if the number of the additional constraints is comparitively small. The algorithm has been tested on a IBM 7040 (16 K) computer. A Fortran IV program is included in the appendix.
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