Research in Scientific Computing in Undergraduate Education

A spectral collocation method for singularly perturbed hyperbolic equations and its application to a point particle around a Schwarzschild black hole

We consider a hyperbolic conservation law with singular source terms which involve the dirac delta function or its derivative. Preliminary results of a convergence study of the spectral collocation method are presented. For a linear hyperbolic equation with a delta function source term, the spectral collocation methods can yield fast convergence without regularization, due to a novel cancellation of oscillations on collocation grid points. The linear wave equation obtained for a Schwarzschild black hole is solved using the spectral collocation method. Wave forms produced under these conditions are a primary source for gravitational wave detectors such as LISA and LIGO. The result of the spectral collocation methods in this situation is also compared to commonly used finite-difference methods such the Lax-Wendroff scheme.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: