59925297
FORTRAN-SC, A FORTRAN Extension for engineering/scientific computation with access to ACRITH: language description with examples
The prototype of a new programming language and its implementation are presented. The language, called FORTRAN-SC (FORTRAN for Scientific Computation), is an extension of FORTRAN 77. It is particularly suitable for developing numerical algorithms which deliver highly accurate and automatically verified results. Many concepts proposed for the FORTRAN 8x standard are available in FORTRAN-SC. In addition, interval and vector/matrix arithmetic are predefined. The mathematical properties of all arithmetic operations are precisely defined in the language. In particular, all predefined operators must be of highest accuracy. The development of FORTRAN-SC was motivated by the need to write numerical algorithms in mathematical notation. The experience with the existing compiler has shown that FORTRAN-SC simplifies programming. Furthermore, it can make numerical programs more reliable.
123298075
Eindeutigkeitssätze für gewöhnliche, parabolische und hyperbolische Differentialgleichungen
122666640
Remarks on a paper by F. Browder about contraction
THROUGHOUT this note, X denotes a complete metric space with distance function d, and T is a map from X into itself. Powers of T are defined by Tax = x and T”+ lx = T(T”x), n 2 0. Occasionally, we use the notation xk = Tkx, in particular x0 = x, x1 = TX, for the sake of brevity. The set {x, TX, T'x, . . . , T”x,. . .} is called an orbit (starting at x) and denoted by O(x). The set 0(x, y) is the union of the two orbits starting at x and y, 0(x, y) = {xk, yk: k 3 O}. The diameter diam A of a nonempty subset A of X is the supremum of the numbers d(x, y), where x and y vary in A. The letter 4 denotes a contractive gauge function, i.e. a continuous, increasing function from R,, the non-negative reals, into R, which satisfies 4(s) 0.
120951143
Verallgemeinerte Laplace-Operatoren und Potentiale
119881926
Fehlerabschätzungen und Eindeutigkeitssätze für gewöhnliche und partielle Differentialgleichungen
122832071
THERE IS AN ELEMENTARY PROOF OF PEANO'S EXISTENCE THEOREM.
Abstract : An elementary, constructive proof of Peano's existence theorem is given. The maximal solution is constructed as a limit of a decreasing sequence of approximate solutions. (Author)
1300115
Flexible precision control and dynamic data structures for programming mathematical and numerical algorithms