@TechReport{	  it:2006-021,
  author	= {Gunilla Linde and Jonas Persson and von Sydow, Lina},
  title		= {High-Order Adaptive Space-Discretizations for the
		  {B}lack--{S}choles Equation},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2006},
  number	= {2006-021},
  month		= apr,
  abstract	= {In this paper we develop a high-order adaptive finite
		  difference space-discretization for the Black--Scholes
		  (B--S) equation. The final condition is discontinuous in
		  the first derivative yielding that the effective rate of
		  convergence is two, both for low-order and high-order
		  standard finite difference (FD) schemes. To obtain a
		  sixth-order scheme we use an extra grid in a limited space-
		  and time-domain. The new sixth-order method is called
		  FD6G2. The FD6G2-method is combined with space- and
		  time-adaptivity to further enhance the method. To obtain
		  solutions of high accuracy in several dimensions the
		  adaptive FD6G2-method is superior to both standard and
		  adaptive second-order FD-methods.}
}