High order smoothing schemes for inhomogeneous parabolic problems with applications in option pricing

A new family of numerical schemes for inhomogeneous parabolic partial differential equations is developed utilizing diagonal Pide schemes combined with positivity-preserving Pade schemes as damping devices. We also develop a split version of the algorithm using partial fraction decomposition to address difficulties with accuracy and computational efficiency in solving and to implement the algorithms in parallel. Numerical experiments are presented for several inhomogeneous parabolic problems, including pricing of financial options with nonsmooth payoffs. (c) 2007 Wiley Periodicals, Inc.