Recent content by omyojj

hmm..can you elaborate on the iterating scheme of recursion eq. or share some links I can refer to?

second ODE, initial conditions are zeros at infinity! I want to know the temperature profile of phase transition layer in the interstellar medium. For stationary solution, the dimensionless differential equation I ended up with is \frac{d^2T}{dx^2} = \frac{f(T)}{T^2} - \frac{1}{T} where f(T)...

While dealing with a wave problem, I encountered the following equation \frac{d}{dx}\left[(1-x^2)^2\frac{d}{dx}y\right] - k^2y = -\omega^2y with x ∈ [0,A], (0<A<=1) where k is a real number. Thus it has eigenvalue ω^2 and weight unity. Boundary conditions are \frac{dy}{dx}...

No. Maybe I should explain the background to this problem. I encountered the above equation while solving the p-mode(acoustic wave) dispersion relation in an horizontally infinite isothermal disk with vertical stratification in the z direction. Boundary conditions are chosen so that vertical...

One thing I tried is to integrate the above equation from x=0 to x=a to get \lambda_n \int_0^a y_n dx = k^2 \int_0^a y_n dx (The first term on the left-hand side vanished from the given boundary conditions. Hence, \lambda_n = k^2 which is strange because all the eigenvalues are given as λ_n...

I'm trying to solve the following Sturm-Liouville system \frac{d}{dx}\left((1-x^2)^2\frac{d}{dx}y\right) + (\lambda - k^2)y=0 defined in an interval -a<x<a (or 0<x<a) with 0<a<=1. Here, k is a real number and λ is the eigenvalue of the system. y satisfies boundary conditions...

Oops, I committed an error...was going to say 'this is NOT a homework problem'.. x = \mathrm{tanh}u and the resulting equation is the associated Legendre's equation. Thank you anyway, I should've examined the equation with more patience..

Could you please help me or give me any hint to solve this ODE.. \frac{d^2y}{d x^2} + ( 2\rm{sech}^2 x - a^2 ) y = 0 where a is a constant. I want only even function solution. (y(x) = y(-x)) BTW, this is a homework problem. I encountered this equation while considering surface waves...

Ok.. What if I simplify the problem? \left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial z^2} \right) \psi(x, z) = \theta(z - ( a + \epsilon \cos(kx) ) } If I can solve the above one then the superposed solution can be obtained. help me. T.T

Hi, While considering perturbed gravitational potential of incompressible fluid in rectangular configuration, I encountered two dimensional Poisson's equation including the step function. I want to solve this equation \left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial z^2}...

I'm doing an undergrad research job.. I have encountered the following coupled 2nd order linear ODE with constant coefficients a, b, c, d... \begin{align} \frac{d^2 y_1}{d x^2} + a^2y_1 & = -c y_2 \\ \frac{d^2 y_2}{d x^2} - b^2y_2 & = -d y_1 \end{align} In addition, I...

suppose that the prescribed magnetic field \mathbf{B} = B_0 \hat{\mathbf{z}} is present..and suppose that ,at time t, at the origin of the inertial frame, a particle with charge q moves along the y-direction with velocity u..then the Lorentz force due to magnetic field is in the...

I beg you to understand my poor Eng.. If there is any poor grammar or spelling..please correct me.. While studying MHD with "An Introduction to Magnetohydrodynamics" written by Davidson, I encountered the term 'current density'.. As you know well, empirically, \mathbf{J} = \sigma...

sorry..Now I can type LaTex a little I think that one of the possible ways to get the right answer is.. \int_{-\infty}^{\infty} \frac{e^{-x^2}}{x^2+a^2} dx = 2 \int_{0}^{\infty} \frac{e^{-x^2}}{x^2+a^2} dx = 2e^{a^2} \int_{a}^{\infty} \frac{e^{-x^2}}{x\sqrt{x^2-a^2}} by substituting...

re [tex]\int -\infty^\infty frac{e^{-x^2}{x^2+a^2}dt[\tex]