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  • 1
    Electronic Resource
    Electronic Resource
    Order, stepsize and stiffness switching (1990)
    Springer
    Computing 44 (1990), S. 209-220 
    Details
    ISSN: 1436-5057
    Keywords: 65L05 ; Order ; stepsize ; stiffness ; automatic switching
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir diskutieren die Frage: “Wann soll ein Programm zwischen steifen und nicht-steifen Verfahren wählen, wann soll es die Ordnung ändern und in welcher Weise soll es die Größe des nächsten Schrittes bestimmen?” Kriterien für die Auswahl zwischen verschiedenen Möglichkeiten, die sich im Verlauf der Integration ergeben, werden vorgeschlagen und in algorithmischer Form dargestellt.
    Notes: Abstract The question discussed in this paper is “When should a code switch between stiff and non-stiff options, when should it switch between one order and another and how should it adjust its stepsize from one step to the next.” Criteria are proposed for switching between the options that become available as the integration progresses and these are presented in algorithmic form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02262217
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  • 2
    Electronic Resource
    Electronic Resource
    A transformation for the analysis of DIMSIMs (1994)
    Springer
    BIT 34 (1994), S. 25-32 
    Details
    ISSN: 1572-9125
    Keywords: 65L05 ; general linear method ; diagonally implicit method ; DIMSIM ; order conditions ; stability polynomial
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The special case of diagonally-implicit multistage integration methods is considered in which the order, the stage order, the number of values passed between steps and the number of stages in a step, all coincide. It is shown that a similarity transformation can be applied to the matrices characterizing the method so as to simplify the expression for the stability polynomial and thus aid in the search for methods with acceptable stability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01935014
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  • 3
    Electronic Resource
    Electronic Resource
    A generalization of singly-implicit methods (1981)
    Springer
    BIT 21 (1981), S. 175-189 
    Details
    ISSN: 1572-9125
    Keywords: 5.17 ; 65L05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Singly-implicit Runge-Kutta methods are characterized by a one-point spectrum property of the coefficient matrix. If a method of this type is also a collocation method, then its abscissae are proportional to the zeros of a Laguerre polynomial. The generalization introduced here is a multistep method in the style of Nordsieck and also a multistage method under the one-point spectrum constraint. It is found that much of the theory of singly-implicit methods carries over but with Laguerre polynomials replaced by their usual generalizations. Amongst the formal properties of the new method which are studied is a derivation of the similarity transformations which allow their efficient implementation. A preliminary investigation is made of the stability of the new methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933162
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  • 4
    Electronic Resource
    Electronic Resource
    Diagonally implicit general linear methods for ordinary differential equations (1993)
    Springer
    BIT 33 (1993), S. 452-472 
    Details
    ISSN: 1572-9125
    Keywords: AMS(MOS) ; 65L05 ; 65L07 ; General linear method ; order conditions ; stability analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate some classes of general linear methods withs internal andr external approximations, with stage orderq and orderp, adjacent to the class withs=r=q=p considered by Butcher. We demonstrate that interesting methods exist also ifs+1=r=q, p=q orq+1,s=r+1=q, p=q orq+1, ands=r=q, p=q+1. Examples of such methods are constructed with stability function matching theA-acceptable generalized Padé approximations to the exponential function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01990528
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  • 5
    Electronic Resource
    Electronic Resource
    On symmetrizers for Gauss methods (1991)
    Springer
    Numerische Mathematik 60 (1991), S. 465-476 
    Details
    ISSN: 0945-3245
    Keywords: 65L05 ; 65L20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper the maximum attainable order of a special class of symmetrizers for Gauss methods is studied. In particular, it is shown that a symmetrizer of this type for thes-stage Gauss method can attain order 2s-1 only for 1 ≦s ≦ 3, and that these symmetrizers areL-stable. A classification of the maximum attainable order of symmetrizers for some higher stages is presented. AnL-stable symmetrizer is also shown to exist for each of the methods studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385731
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  • 6
    Electronic Resource
    Electronic Resource
    Some orbital test problems (1994)
    Springer
    Computing 53 (1994), S. 75-94 
    Details
    ISSN: 1436-5057
    Keywords: 65L05 ; Periodic orbits ; test problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Probleme mit periodischen Lösungen eignen sich besonders als Testprobleme für Software zur Behandlung von Differentialgleichungen, da sie es leicht ermöglichen, die Genauigkeit der berechneten Ergebnisse zu beurteilen. Selbst der Lauf eines einzigen Planeten um die schwere Sonne ist nützlich als Testproblem, da Umlaufbahnen mit sich ändernder Exzentrizität wechselnde Anforderungen an die numerische Software stellen. Die Umlaufbahnen, die hier betrachtet werden, gründen sich auf genau diesem einfachen Problem, jedoch mit dem wesentlichen Unterschied, daß der Abstand zwischen Planet und Sonne mit der Norm ‖ . ‖∞ anstelle der üblichen Euclid'schen Norm ‖ . ‖2 gemessen wird. Insbesondere untersuchen wir Umlaufbahnen basierend auf jedem der Differentialgleichungssysteme $$X = \nabla \left( {\frac{1}{{\left\| X \right\|}}} \right)$$ und $$X = - \frac{1}{{\left\| X \right\|^3 }}.$$ Ein Merkmal beider dieser Systeme, wenn die Norm ‖ . ‖∞ verwendet wird, ist das Auftreten von Unstetigkeiten in höheren Ableitungen der Lösung. Hierin begründet sich ihr potentieller Wert als schwierige Testprobleme. Im Hinblick auf diese Anwendung werden einige periodische Lösungen aufgezeigt. Es wird gezeigt, daß das zweite der beiden in diesem Papier betrachteten Differentialgleichungssysteme, bei beliebiger Wahl der Norm, periodische Umlaufbahnen besitzt.
    Notes: Abstract Problems with periodic solutions are convenient as test problems for differential equation software because of the ease with which the accuracy of computed results can be assessed. Even the motion of a single planet around a heavy sun is useful as a test problem because orbits of varying eccentricity make varying demands on numerical software. The orbits discussed here are based on this same simple problem but with the essential difference that the distance from the planet to the sun is based on the norm ‖ . ‖∞ rather than the usual Euclidean norm ‖ . ‖2. Specifically, we explore orbits based on each of the differential equation systems $$X = \nabla \left( {\frac{1}{{\left\| X \right\|}}} \right)$$ and $$X = - \frac{1}{{\left\| X \right\|^3 }}.$$ A feature of both these systems, when the ‖ . ‖∞ norm is used, is the occurrence of discontinuities in the higher derivatives of the solution. This is why they have a potential value as difficult test problems. With this application in mind, some periodic solutions are identified. For an arbitrary choice of norm, the second of the two differential equation systems considered in this paper is shown to possess periodic orbits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02262109
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  • 7
    Electronic Resource
    Electronic Resource
    Experiments with a variable-order type 1 DIMSIM code (1999)
    Springer
    Numerical algorithms 22 (1999), S. 237-261 
    Details
    ISSN: 1572-9265
    Keywords: DIMSIM methods ; Nordsieck representation ; local error estimation ; step size and order changing strategy ; 65L05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The issues related to the development of a new code for nonstiff ordinary differential equations are discussed. This code is based on the Nordsieck representation of type 1 DIMSIMs, implemented in a variable-step size variable-order mode. Numerical results demonstrate that the error estimation employed in the code is very reliable and that the step and order changing strategies are very robust. This code outperforms the Matlab ode45 code for moderate and stringent tolerances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019135630307
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  • 8
    Electronic Resource
    Electronic Resource
    DESIRE: diagonally extended singly implicit Runge–Kutta effective order methods (1998)
    Springer
    Numerical algorithms 17 (1998), S. 121-145 
    Details
    ISSN: 1572-9265
    Keywords: implicit Runge–Kutta methods ; singly-implicit methods ; effective order ; 65L05 ; 65L06
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract To overcome known disadvantages in the use of singly-implicit methods in the solution of stiff differential equations, two generalizations have been recently introduced. These are the use of additional diagonally-implicit stages and the use of effective order as a weakening of the conditions on the method. In this paper, these two generalizations are combined into a unified scheme. The resulting DESIRE methods are very promising alternatives to standard methods for solving stiff problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011623226983
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  • 9
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    Complete development of mosquito phases of the malaria parasite in vitro (2002)
    American Association for the Advancement of Science (AAAS)
    Details
    Publication Date: 2002-01-26
    Description: Methods for reproducible in vitro development of the mosquito stages of malaria parasites to produce infective sporozoites have been elusive for over 40 years. We have cultured gametocytes of Plasmodium berghei through to infectious sporozoites with efficiencies similar to those recorded in vivo and without the need for salivary gland invasion. Oocysts developed extracellularly in a system whose essential elements include co-cultured Drosophila S2 cells, basement membrane matrix, and insect tissue culture medium. Sporozoite production required the presence of para-aminobenzoic acid. The entire life cycle of P. berghei, a useful model malaria parasite, can now be achieved in vitro.〈br /〉〈span class="detail_caption"〉Notes: 〈/span〉Al-Olayan, Ebtesam M -- Beetsma, Annette L -- Butcher, Geoff A -- Sinden, Robert E -- Hurd, Hilary -- New York, N.Y. -- Science. 2002 Jan 25;295(5555):677-9.〈br /〉〈span class="detail_caption"〉Author address: 〈/span〉Centre for Applied Entomology and Parasitology, School of Life Sciences, Keele University, Staffordshire ST5 5BG, UK.〈br /〉〈span class="detail_caption"〉Record origin:〈/span〉 〈a href="http://www.ncbi.nlm.nih.gov/pubmed/11809973" target="_blank"〉PubMed〈/a〉
    Keywords: 4-Aminobenzoic Acid/pharmacology ; Aedes ; Aerobiosis ; Animals ; Anopheles/parasitology ; Cell Line ; Coculture Techniques ; Collagen ; Culture Media ; Drosophila ; Drug Combinations ; Hydrogen-Ion Concentration ; Laminin ; Life Cycle Stages ; Malaria/parasitology ; Male ; Mice ; Plasmodium berghei/cytology/drug effects/*growth & development ; Proteoglycans
    Print ISSN: 0036-8075
    Electronic ISSN: 1095-9203
    Topics: Biology , Chemistry and Pharmacology , Computer Science , Medicine , Natural Sciences in General , Physics
    Published by American Association for the Advancement of Science (AAAS)
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  • 10
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    A hub-and-spoke circuit drives pheromone attraction and social behaviour in C. elegans (2009)
    Nature Publishing Group (NPG)
    Details
    Publication Date: 2009-04-08
    Description: Innate social behaviours emerge from neuronal circuits that interpret sensory information on the basis of an individual's own genotype, sex and experience. The regulated aggregation behaviour of the nematode Caenorhabditis elegans, a simple animal with only 302 neurons, is an attractive system to analyse these circuits. Wild social strains of C. elegans aggregate in the presence of specific sensory cues, but solitary strains do not. Here we identify the RMG inter/motor neuron as the hub of a regulated circuit that controls aggregation and related behaviours. RMG is the central site of action of the neuropeptide receptor gene npr-1, which distinguishes solitary strains (high npr-1 activity) from wild social strains (low npr-1 activity); high RMG activity is essential for all aspects of social behaviour. Anatomical gap junctions connect RMG to several classes of sensory neurons known to promote aggregation, and to ASK sensory neurons, which are implicated in male attraction to hermaphrodite pheromones. We find that ASK neurons respond directly to pheromones, and that high RMG activity enhances ASK responses in social strains, causing hermaphrodite attraction to pheromones at concentrations that repel solitary hermaphrodites. The coordination of social behaviours by RMG suggests an anatomical hub-and-spoke model for sensory integration in aggregation, and points to functions for related circuit motifs in the C. elegans wiring diagram.〈br /〉〈br /〉〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2760495/" target="_blank"〉〈img src="https://static.pubmed.gov/portal/portal3rc.fcgi/4089621/img/3977009" border="0"〉〈/a〉   〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2760495/" target="_blank"〉This paper as free author manuscript - peer-reviewed and accepted for publication〈/a〉〈br /〉〈br /〉〈span class="detail_caption"〉Notes: 〈/span〉Macosko, Evan Z -- Pokala, Navin -- Feinberg, Evan H -- Chalasani, Sreekanth H -- Butcher, Rebecca A -- Clardy, Jon -- Bargmann, Cornelia I -- CA24487/CA/NCI NIH HHS/ -- F32 GM077943/GM/NIGMS NIH HHS/ -- F32 GM077943-03/GM/NIGMS NIH HHS/ -- GM07739/GM/NIGMS NIH HHS/ -- GM077943/GM/NIGMS NIH HHS/ -- R01 CA024487/CA/NCI NIH HHS/ -- R01 CA024487-30/CA/NCI NIH HHS/ -- T32 GM007739/GM/NIGMS NIH HHS/ -- T32 GM007739-30/GM/NIGMS NIH HHS/ -- Howard Hughes Medical Institute/ -- England -- Nature. 2009 Apr 30;458(7242):1171-5. doi: 10.1038/nature07886. Epub 2009 Apr 6.〈br /〉〈span class="detail_caption"〉Author address: 〈/span〉Howard Hughes Medical Institute, Laboratory of Neural Circuits and Behavior, The Rockefeller University, 1230 York Avenue, New York, New York 10065, USA.〈br /〉〈span class="detail_caption"〉Record origin:〈/span〉 〈a href="http://www.ncbi.nlm.nih.gov/pubmed/19349961" target="_blank"〉PubMed〈/a〉
    Keywords: Animals ; Caenorhabditis elegans/cytology/drug effects/*physiology ; Caenorhabditis elegans Proteins/genetics/metabolism ; Disorders of Sex Development ; Feeding Behavior/drug effects/physiology ; Male ; Models, Neurological ; Mutation ; Neural Pathways/drug effects/*physiology ; Neurons/drug effects/physiology ; Pheromones/pharmacology/*physiology ; Receptors, Neuropeptide Y/genetics/metabolism ; *Social Behavior
    Print ISSN: 0028-0836
    Electronic ISSN: 1476-4687
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Published by Nature Publishing Group (NPG)
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