Results 221 to 230 of about 23,073 (264)

Linear Ordinary Differential Equations

1986
This is the first of two chapters concerning linear systems and equations. We have already established the unique existence of solutions to initial value problems concerning them. However, because of their linear nature we can say much more by using the framework of the linear space.
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Classification of Linear Ordinary Differential Equations: II

Differential Equations, 2002
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On the differential invariants of a linear ordinary differential equation

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1981
SynopsisLety(n)+a1y(n−1+…+an−1y(1)+an= 0 (*) be a linear ordinary differential equation of ordern. A (relative) differential invariant of (*) is a differential polynomial function π(xi) defined on the solution space of (*) satisfying: there is an integergsuch that for all invertible linear transformations α ofVinto itself, π(αxi) = (det α)βπ(xi).
Kung, Joseph P. S., Rota, Gian-Carlo
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General linear methods for ordinary differential equations

Mathematics and Computers in Simulation, 2009
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A factorization algorithm for linear ordinary differential equations

Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89, 1989
The reducibility and factorization of linear homogeneous differential equations are of great theoretical and practical importance in mathematics. Although it has been known for a long time that factorization is in principle a decision procedure, its use in an automatic differential equation solver requires a more detailed analysis of the various steps ...
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The Classification of Linear Ordinary Differential Equations: I

Differential Equations, 2002
This paper is concerned with the classification of \(n\)th-order \((n\geq 3)\) linear ODEs with respect to contact transformations. Using the coincidence of contact symmetries with point symmetries for \(n> 3\) and the invariance of the number of point symmetries under contact transformations for \(n\geq 3\) (see, the author [Russ. J. Math. Phys.
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Nonbounded solutions of linear ordinary differential equations

Mathematical Notes of the Academy of Sciences of the USSR, 1984
For the differential equation \(u^{(n)}+p(t)u=0\) conditions on p are given for the existence of unbounded solutions.
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Linear Ordinary Differential Equations

1983
In this chapter we shall present a systematic study of the solutions of linear ordinary differential equations. Such equations continue to play an important role in many branches of the natural sciences and other fields, e.g., economics, so that they may be treated here in their own right. On the other hand, we should not forget that our main objective
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Ordinary Differential Equations and Linear Systems of Ordinary Differential Equations

2022
Mohammad Ashraf, Vincenzo De Filippis, Mohammad Aslam Siddeeque   +2 more
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Hecke Operators on Linear Ordinary Differential Equations

Acta Applicandae Mathematica, 1999
The theory of automorphic forms and that of ordinary linear differential equations are closely related. Automorphic forms are common eigenforms of certain Hecke operators. Thus it is natural to consider the Hecke operators acting on the space of ordinary differential equations associated with automorphic forms.
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