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Ordinary Differential Equations [PDF]

Technometrics, 1975
Many problems of higher analysis presuppose a knowledge of ordinary differential equations; for example, problems of potential theory, of the calculus of variations, of theoretical physics and of partial differential equations (see Chapter 37.). Beyond this, a wide field of applications is opened up by ordinary differential equations; for example, the ...
W. Gellert, H. Küstner, H. Kästner, S. Gottwald, M. Hellwich   +4 more
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Ordinary Differential Equations [PDF]

, 2009
In this chapter we will introduce some notions and methods related to ordinary differential equations (ode). We study different representations of the solutions to odes, the singular points and the plane phases of planar odes, and an example of an ode with five equilibrium points.
Tsuneyoshi Nakayama, Hiroyuki Shima
  +7 more sources

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Ordinary Differential Equations

The American Mathematical Monthly, 1971
When the derivative y’ = f’(t) of an unknown function y = f(t) is given, we usually have to find the antiderivative. We treated this problem in Sections 9.3 and 9.5. Sometimes the derivative y’ is not given as a function of t, but is involved in an equation which contains also the unknown function y = f(t). As an example, consider the equation $$y'
Ray Redheffer, Jack K. Hale
openaire   +4 more sources

Ordinary Differential Equations [PDF]

, 1980
Many problems in applied mathematics lead to ordinary differential equations. In the simplest case one seeks a differentiable function y = y(x) of one real variable x, whose derivative y′(x) is to satisfy an equation of the form y′(x) = f(x, y(x)), or more briefly, $$y' = f\left( {x,y} \right)$$ (7.0.1) one then speaks of an ordinary ...
J. Stoer, R. Bulirsch
openaire   +1 more source

Ordinary Differential Equations

2012
In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice.
Claudia Valls, Luis Barreira
openaire   +5 more sources

Cause and cure of sloppiness in ordinary differential equation models.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied.
C. Tönsing, J. Timmer, C. Kreutz
semanticscholar   +1 more source

Direct and Adjoint Sensitivity Analysis of Ordinary Differential Equation Multibody Formulations

Journal of Computational and Nonlinear Dynamics, 2014
Sensitivity analysis of multibody systems is essential for several applications, such as dynamics-based design optimization. Dynamic sensitivities, when needed, are often calculated by means of finite differences.
D. Dopico, Yitao Zhu, Adrian Sandu, C. Sandu   +3 more
semanticscholar   +1 more source

Deriving age‐specific incidence from prevalence with an ordinary differential equation

Statistics in Medicine, 2013
This article describes new relationships between the age‐specific incidence of, the prevalence of and mortality from a chronic disease. We express these relationships in terms of an ordinary differential equation and form the methodological basis for a ...
R. Brinks, S. Landwehr, A. Icks, M. Koch, G. Giani   +4 more
semanticscholar   +1 more source

LSODE and LSODI, two new initial value ordinary differential equation solvers

SGNM, 1980
Two new packages are available for the numerical solution of the initial value problem for stiff and nonstiff systems of ordinary differential equations (ODE's).
A. Hindmarsh
semanticscholar   +1 more source