Recent content by SarthakC

And how do you prove this statement? I would be more inclined to believe it to be ##\frac{1}{2}\delta##, instead. But i can't prove that either.

Um.. Could you elaborate on how this helps?

It isn't really translation. the Theta function makes a reasonable difference. And I'm evaluatig both funcitons without any delay. Could you elaborate how it is a case of translation? The integral is coming about in my attempts to solve a differential equation of a particular form (I had asked...

Hi, Is the following integral well defined? If it is, then what does it evaluate to? \int_{-1}^{1} \delta(x) \Theta(x) \mathrm{d}x where \delta(x) is the dirac delta function, and \Theta(x) is the the Heaviside step function. What about if I choose two functions f_k and g_k, which are...

Thanks! I'll give both the spectral method and the finite difference method a shot and try to solve my original problem. I'll get back to you guys if I have any more clarifications! Thanks!

Hmm. So the idea is I use the finite difference method and the boundary conditions to give me an algebraic problem which I then solve numerically to get all the ##x_i##s?

Could someone give me an example? For example let's just take a simple first order equation of $$y^\prime + \Theta(x) y = 0$$ where ##\Theta(x)## is the Heaviside step function, with a domain from ##(-\pi,\pi)##, with peridic boundary equations. Could anyone just show me a few steps from where I...

Umm... Maybe I should make my specific scenario a little clearer. My differential equation is of the form $$f(x) \partial_x^2 y + g(x) \partial_x y + h(x) y =0$$ In this scenario, replacing ##y## with a Fourier series in ##x## is not really useful, because the functions ##f, g## and ##h## do...

Hi, Are there any numerical techniques I can use to solve differential equations with periodic boundary conditions? I know of several techniques for other kinds of boundary conditions (such as Runge-Kutta method, Euler method etc.), but I am interested in knowing how to numerially solve...

Is it possible to solve a differential equation of the following form? $$\partial_x^2y + \delta(x) \partial_x y + y= 0$$ where ##\delta(x)## is the dirac delta function. I need the solution for periodic boundary conditions from ##-\pi## to ##\pi##. I've realized that I can solve this for some...