Weighted quadrature in Krylov methods
Abstract
The Krylov subspace approximation techniques described by Gallopoulos and Saad [2] for the numerical solution of parabolic partial differential equations are extended. By combining the weighted quadrature methods of Lawson and Swayne [6] with Krylov subspace approximations, three major improvements are made. First, problems with time-dependent sources or boundary conditions may be solved more efficiently. Second, methods are derived which have the stability properties (such as A-stability) of the underlying rational approximation to the exponential function. Third, it is possible to present methods which are robust under space discretization refinement. In particular, a fixed precision is essentially maintained for the same time integration method and for constant values of the parameters, when the spatial resolution is increased.
