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Generalized higher-order differentiation [PDF]

Acta Applicandae Mathematicae, 1989
For some time now the first two authors have been developing a theory of ``higher order tensors'' which they call (derivative) strings. This work has been motivated by examples from statistics where such objects occur naturally. By a ``higher order tensor'' is meant an object like a tensor but whose transformation rule under a change of co-ordinates ...
Barndorff-Nielsen, O. E., Blæsild, P., Mora, M.   +2 more
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Higher-order differential equations and higher-order lagrangian mechanics

Mathematical Proceedings of the Cambridge Philosophical Society, 1986
The study of higher-order mechanics, by various geometrical methods, in the framework of the theory of higher-order tangent bundles or jet spaces, has been undertaken by a number of authors recently: for example, Tulczyjew [16, 17], Rodrigues [14, 15] de León [8], Krupka and Musilova [11, and references therein].
Willy Sarlet, M. Crampin, Frans Cantrijn
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Applications of Higher Order Differential Equations

1993
Publisher Summary This chapter provides an overview of applications of higher order differential equations. It reviews the procedures that lead to the differential equations that model simple harmonic motion and damped motion. Another situation that leads to a second order ordinary differential equation is that of the simple pendulum.
Martha L. Abell, James P. Braselton
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Higher order pseudospectral differentiation matrices

Applied Numerical Mathematics, 2005
``We approximate the derivatives of a function \(f(x)\) by interpolating the function with a polynomial at the Chebyshev extrema nodes \(x_k\), differentiating the polynomial, and then evaluating the polynomial at the same nodes.'' The paper investigates the roundoff properties of various ways of setting up the matrix that maps the vector \(\bigl(f(x_k)
Elsayed M. E. Elbarbary, Salah M. El-Sayed   +1 more
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Higher order differential structure of images

Image and Vision Computing, 1993
This paper is meant as a tutorial on the basic concepts for vision in the ‘Koenderink’ school. The concept of scale-space is a necessity, if the extraction of structure from measured physical signals (i.e. images) is at stage. The Gaussian derivative kernels for physical signals are then the natural analogues of the mathematical differential operators.
Luc Florack, Alfons H. Salden, Bart M. ter Haar Romeny, Max A. Viergever   +3 more
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Higher-Order Differential Equations

2011
High-order differential equations often arise from mathematical modeling of a variety of physical phenomena. For example, higher even-order differential equations may appear in astrophysics, structural mechanics and geophysics, and higher odd-order differential equations, such as the Korteweg-de Vries (KdV) equation, are routinely used in modeling ...
Tao Tang, Li-Lian Wang, Jie Shen
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Viability Theorems for Higher-Order Differential Inclusions [PDF]

Set-Valued Analysis, 1998
The authors prove a necessary and sufficient condition for the existence of viable solutions to an \(n\)th-order differential inclusion in a finite-dimensional Banach space.
J. Alberto Murillo, Luis Marco
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Higher order differential solutions

1992
In this chapter we adopt a different perspective for attacking the inverse scattering problem. It has been shown in previous chapters how the wave equation can be transformed into an integral equation and how, by making two separate linearizations, first for the scattered field and second for the variations of the scatterer itself, the integral ...
K. I. Hopcraft, P. R. Smith
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Higher-Order Differential Calculi [PDF]

, 2015
In this section, we will construct a higher-order differential calculus (HODC) provided that we are given a first-order differential calculus (FODC). This construction will be a functor. What we will construct are the differentials in the braided exterior algebra that are analogous to the de Rham differentials in the classical case.
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Higher-Order Differential Equations

2019
Through our study of linear systems of differential equations, we have already encountered higher-order differential equations that arise naturally in physical applications. Two particularly important ones are those associated with spring-mass systems and RLC circuits. Here we briefly revisit these equations.
Merle C. Potter, Allan Struthers
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