This report discusses an implementation [1] of an Adaptive Mesh Refinement (AMR) Poisson solver which solves Poisson’s equation using multigrid relaxation. Local refinement introduces several added issues. Special care has been taken to match the solution across coarse/fine interfaces so that the solution maintains global second order accuracy. The nested mesh hierarchy can be defined by the us...

In this paper we study the existence of a formal series expansion of the error of spline Petrov–Galerkin methods applied to a class of periodic pseudodifferential equations. From this expansion we derive some new superconvergence results as well as alternative proofs of already known weak norm optimal convergence results. As part of the analysis the approximation of integrals of smooth function...

In the present investigation, the fully implicit and Crank–Nicolson difference schemes for solving option prices are analyzed. It is proved that the error expansions for the difference methods have the correct form for applying Richardson extrapolation to increase the order of accuracy of the approximations. The difference methods are applied to European, American, and down-and-out knock-out ca...

Assume that the initial value vector s R ∈  is given. The exact solution ) t ( y of the system defined by (1) is normally not known. Therefore, it is convenient to apply a suitable numerical method in order to calculate some sufficiently accurate approximate values of the components of the exact solution vector ) t ( y at the grid-points belonging to some discrete set of values of the time-var...

In this paper,we consider theCOSmethod for pricing European andBermudan options under the stochastic alpha beta rho (SABR) model. In the COS pricing method, we make use of the characteristic function of the discrete forward process. We observe second-order convergence by using a second-order Taylor scheme in the discretization, or by using Richardson extrapolation in combination with a Euler–Ma...

Ligands of the aroylhydrazone class have shown much promise as potential chelators for treatment of iron overload disease and perhaps cancer (Johnson et al., 1982; Baker et al., 1992; Richardson et al., 1995; Richardson & Milnes, 1997). Our previous investigations have demonstrated that 2-hydroxy-1naphthaldehyde isonicotinoyl hydrazone, (II), and several other aroylhydrazone chelators possess a...