969 resultados para Differential equations, Partial -- Numerical solutions -- Computer programs


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Based on the author's thesis, Yale.

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"C00-1469-0118."

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"COO-2383-0036."

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"Presented at the Differential Equation Workshop, Center for Interdisciplinary Research (Zif), University of Bielefeld, West Germany, April 21, 1980."

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Bibliography: leaf 11.

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Available on demand as hard copy or computer file from Cornell University Library.

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pt. I. (Vol. I) Exact equations and Pfaff's problem. 1890.--pt. II. (Vol. II-III) Ordinary equations, not linear. 1900.--pt. III. (Vol. IV) Ordinary equations. 1902.--pt. IV (vol. V-VI) Partial differential equations. 1906.

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Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

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First-year undergraduate engineering students' understanding of the units of factors and terms in first-order ordinary differential equations used in modelling contexts was investigated using diagnostic quiz questions. Few students appeared to realize that the units of each term in such equations must be the same, or if they did, nevertheless failed to apply that knowledge when needed. In addition, few students were able to determine the units of a proportionality factor in a simple equation. These results indicate that lecturers of modelling courses cannot take this foundational knowledge for granted and should explicitly include it in instruction.

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Some oscillation criteria for solutions of a general perturbed second order ordinary differential equation with damping (r(t)x′ (t))′ + h(t)f (x)x′ (t) + ψ(t, x) = H(t, x(t), x′ (t)) with alternating coefficients are given. The results obtained improve and extend some existing results in the literature.

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Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

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A dichotomysimilar property for a class of homogeneous differential equations in an arbitrary Banach space is introduced. By help of them, existence of quasi bounded solutions of the appropriate nonhomogeneous equation is proved.

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MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37

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MSC 2010: 26A33, 44A45, 44A40, 65J10