Recent content by dev00790

I've amended your equations, so they are viewable.

Ok, so I try and do this transformation: Using w(z)=y(x(z)), I get w'(z) = y'(x(z)).x'(z) = [y'(x(z))]/p(x) using \frac{dx(z)}{dx}=\frac{1}{p(x)} Thus w''(z) = y'(x(z)).x''(z) + x'(z).y''(x(z)) I cannot see how u arrive at \frac{d^2w}{dz^2}+\lambda^2 p^{-1}w=0 though? Please explain this in...

Bob_for_short, the following point you made; but this is not the same equation as the one above: \frac{\partial}{\partial x}\left(p(x)\frac{dy}{dx}\right) + \lambda^2 y(x)= 0 Can one apply a transformation of variables to this equation as it involves partial differentiation? If so what would...

I've been using a WKB ansatz to deduce a recurrence relation in terms of Y_n and Y_n{'} and hence formulae for Y_n, as its the method I have been using to derive an asymptotic expansion of y(x,\lambda) as n tends to infinity for the following equation: y^{''}+ \lambda^2 p(x)y= 0. This gave the...

Could try Short step Fourier method (SSFM)?

These two below should help. Use the first to classify which type of equation you have, then the second for a method for solving that type. http://en.wikipedia.org/wiki/Integral_equations http://eqworld.ipmnet.ru/en/solutions/ie.htm

Above post is edited, including further working and my question. Replying to your question. I've checked my working, and i believe \frac{\partial^2 u}{\partial t^2} = -\lambda^2 e^{-i\lambda t}y(x) \frac{\partial u}{\partial x} = e^{-i\lambda t}y'(x) Substituting into \frac...

Hello, The differential equation is question that models an elastic string is: \frac {\partial^2 u}{\partial t^2} - \frac{\partial}{\partial x}\left( p(x) \frac{\partial u}{\partial x}\right)= 0 Taking u(x,t) = e^{-i\lambda t} y(x) I simplify above diff.eqn. to: \lambda^2 y(x) +...

Thanks a lot :).

Homework Statement following from this post; https://www.physicsforums.com/showthread.php?t=312075", I would like to know why people generally think the Differential Eigenvalue Problem is interesting? eg why is there a fair amount of current research into this? Homework Equations...

Homework Statement I would like to know what the definition of a Differential Eigenvalue Problem is please? I am a maths undergraduate. Homework Equations \lambda y = L y, where \lambda is eigenvalue, L is a linear operator. The Attempt at a Solution I have searched via google...

Hello, Homework Statement I wondered if someone could help me show / give hints on how to show the (simplified) elastic differential equation (below) is related to the classical Schrodinger equation (in quantum mechanics)? I am a maths undergraduate. 2. Homework Equations - (i had some...