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Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.

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 …
Alan's user avatar
  • 1,594
2 votes
3 answers
2k views

Laurent series expansion for ODE.

OK, then I read Frobenius method in mathworld (I learned when I took ODE 2): http://mathworld.wolfram.com/FrobeniusMethod.html My question is: Are there any ODEs where the solution is given by full L …
Alan's user avatar
  • 1,594
2 votes
0 answers
189 views

Lemma 4.5.1 on page 77 in the book Averaging Methods in Nonlinear Dynamical Systems

I have a query regarding two equalities in the lemma in the book. But first I'll provide two definitions that one needs for this lemma. Definition 4.2.4: Consider the vector field $f(x,t)$ with $f:\ …
Alan's user avatar
  • 1,594
1 vote

Coupled differential equations

I have a suggestion but it's an approximation method. Use Euler method to approximate $x_{n+1}(t)-x_{n}(t)\approx x'_n(t)$. I don't see how you can solve it analytically, beside plugging $x_n(t) = \ …
Alan's user avatar
  • 1,594
0 votes

How to integrate this differential equation?

Well, here's something I thought right now, so it might be wrong (or obviously wrong). You have $$dx/dp=4p^2(p/x+x+5)=4p^2h(p,x)$$ Let's assume we want to have such a function $h(p,x):=h(p/x)$. Then c …
Alan's user avatar
  • 1,594
-1 votes
1 answer
128 views

Proving convergence of an integral-differential equation [closed]

I have a second order nonlinear ordinary differential equation which I transformed into an integral-differential equation by multiplying the ODE by $y'$ and integrating. My question is where can I fi …
Alan's user avatar
  • 1,594