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Results tagged with ca.classical-analysis-and-odes
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user 13904
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
3
votes
1
answer
610
views
Searching for the proof of a certain claim in Arnold's ODE book from 1992
I was reading today the book of Stephen Wiggins called "Global Bifurcations and Chaos" (the 1988 edition).
On pages 12-13 he writes the following:
Consider the following ordinary differential equatio …
- 1,594
0
votes
1
answer
162
views
Iterating the the ODE for Bessel function
If we look at the Bessel ODE:
$$x^2 y'' + xy' + (x^2 - \alpha^2)y = 0$$
Suppose I then put the solution to the above ODE as $J_{\alpha}(x)$ in the RHS, and try to solve the following ODE:
$$x^2 y'' + …
- 1,594
3
votes
1
answer
170
views
Translation to English of Brillouin's analysis of Airy's integral
I am trying to read the following paper by Leon Brillouin (the part on page 16 onwards):
Léon Brillouin, Sur une méthode de calcul approchée de certaines intégrales dite méthode du col, Annales sc …
- 1,594
2
votes
2
answers
211
views
Caratheodory equations
Ok, I am reading Fillipov book on discontinuous right hand side differential equations (the red book).
He states the next lemma:
"
Let the function $f(t,x)$ satisfy the Caratheodory conditions and le …
- 1,594
-4
votes
1
answer
571
views
Derivatives of infinite order [closed]
Is there any sense of taking an infinite number of derivatives? Is it discussed in the literature?
For example, can one make sense of
$$\frac{\partial^{\infty}f(x_1,x_2,\cdots)}{\partial x_1 \partia …
- 1,594
3
votes
0
answers
587
views
Differential Equations vs Difference Equations
My question is:
Is there a duality between a solution of an ODE,PDE,SDE or integral equations with their analog counterpart in the discrete domain?
I mean if I know a solution to the difference equa …
- 1,594
4
votes
1
answer
560
views
Books request on nonlinear recurrence relations.
Hi, do you have some sort of a bibliography on advanced techniques in recurrence equations, such as nonlinear ones and others?
As I see it recurrence equations are quite similar to differential equat …
- 1,594