77 research outputs found
STICAP: A linear circuit analysis program with stiff systems capability. Volume 1: Theory manual
STICAP (Stiff Circuit Analysis Program) is a FORTRAN 4 computer program written for the CDC-6400-6600 computer series and SCOPE 3.0 operating system. It provides the circuit analyst a tool for automatically computing the transient responses and frequency responses of large linear time invariant networks, both stiff and nonstiff (algorithms and numerical integration techniques are described). The circuit description and user's program input language is engineer-oriented, making simple the task of using the program. Engineering theories underlying STICAP are examined. A user's manual is included which explains user interaction with the program and gives results of typical circuit design applications. Also, the program structure from a systems programmer's viewpoint is depicted and flow charts and other software documentation are given
High order stiffly stable linear multistep methods
Stiffly stable linear k-step methods of order k for the initial-value problem are studied. Examples for k = 1, 2, and 3 were discovered by use of Adams-type methods. A large family of stiffly stable linear 7-step methods of order 7 was also found
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
Runge-Kutta methods
Tato práce se zabĂ˝vá Runge--KuttovĂ˝mi metodami pro počáteÄŤnĂ problĂ©m. Práce zaÄŤĂná analĂ˝zou Eulerovy metody a odvozenĂm podmĂnek řádu. Jsou pĹ™edstaveny modifikovanĂ© metody. Pro dvÄ› z nich je urÄŤen jejich řád teoreticky a pro všechny je provedeno numerickĂ© testovánà řádu. Jsou pĹ™edstaveny a numericky testovány dva typy metod s odhadem chyby, "embedded" metody a metody zaloĹľenĂ© na modifikovanĂ˝ch metodách. V druhĂ© části jsou odvozeny implicitnĂ metody. Jsou pĹ™edstaveny dva zpĹŻsoby konstrukce implicitnĂch "embedded" metod. Jsou zmĂnÄ›ny takĂ© diagonálnĂ implicitnĂ metody. Na závÄ›r jsou probrány dva druhy stability u metod prezentovanĂ˝ch v práci.This thesis deals with Runge--Kutta methods for initial value problem. It starts with analysis of Euler method and the order conditions are derived. The modified methods are presented. For two of them is done theoretical examination of order and for all of them, the order is tested numerically. Embedded methods and methods with error estimation based on modified method are presented and numerically tested. In the second part the implicit methods are derived. Then two approaches of constructing implicit embedded methods is presented. Also diagonal implicit method are introduced. Finally, two kinds of stability of presented method is discussed.
ANNUAL REPORT, SEPTEMBER 1, 1970--AUGUST 31, 1971.
This year has seen the completion of initial versions of all programs for the transient analysis of arbitrary networks and the linking together of these packages. A diagram showing the organization of the major parts of the software system is given in Figure 1. A brief description of the purpose of each package is given in section 2 in the report
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SciCADE 95: International conference on scientific computation and differential equations
This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included
Integrated research in constitutive modelling at elevated temperatures, part 1
Topics covered include: numerical integration techniques; thermodynamics and internal state variables; experimental lab development; comparison of models at room temperature; comparison of models at elevated temperature; and integrated software development
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