A numerical method is presented for valuing vanilla American options on a single asset that is up to fourth-order accurate in the log of the asset price, and second-order accurate in time. The method overcomes the standard difficulty encountered in developing high-order accurate finite...

The support operator method designs mimetic finite difference schemes by first constructing a discrete divergence operator based on the divergence theorem, and then defining the discrete gradient operator as the adjoint operator of the divergence based on the Gauss theorem connecting the...

Two types of monotonic properties of solutions of differential equations are discussed and general finite difference schemes, which are stable with respect to these properties are investigated. Apart from being elementary stable, these schemes are also shown to preserve qualitative properties of...

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the...

The state vector is defined for the phase turbulence described by the Kuramoto–Sivashinsky equation. Then the two-time correlation function (TTCF) for the state vector is calculated numerically. In the case when the damping constant is zero, the TTCF decays like Lorentzian. The TTCF changes...

In this paper necessary and sufficient conditions for a multicriteria stochastic control problem are stated. Moreover the convergence of a finite difference approximation method for the solution of the resulting system of second order PDEs is shown. Copyright Springer-Verlag Berlin Heidelberg 2001

In this paper necessary and sufficient conditions for a multicriteria stochastic control problem are stated. Moreover the convergence of a finite difference approximation method for the solution of the resulting system of second order PDEs is shown. Copyright Springer-Verlag Berlin Heidelberg 2001

Two finite-difference methods are constructed and used for the solution of a class of endogenous growth model with physical and human capital. Although both the numerical methods to be developed are implicit by construction, each of the methods can be implemented explicitly. The first method is...