We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines different high-order spatial discretisations with Hundsdorfer and Verwer’s ADI time...

A new method modifying the frequency dependent alternating direction implicit finite difference time domain (FD–ADI– FDTD) is presented. The method can improve the accuracy of FD–ADI–FDTD without significant increase of computational costs. The proposed method is validated by numerical tests. Index Terms ADI–FDTD, Debye media, Accuracy of FDTD

We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general H initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in H towards a dissipative weak solution of Cam...

flood routing has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. floods are taken unsteady flows that vary by time and location. equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional flow the saint-venant hypothesis is considered. dynamic wave model as ...

Spectral factorization is a method of creating causal filters which have causal inverses. I use spectral factorization of an implicit finite-difference stencil of the two-way wave equation approximation in order to model wave propagation by a sequence of deconvolutions. I deconvolve this filter’s coefficients with the wavefield propagating in a constant velocity medium using the helix approach....

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger equation. Although the implicit scheme obtaine...

This study proposes one-dimensional advection–diffusion equation (ADE) with finite differences method (FDM) using implicit spreadsheet simulation (ADEISS). By changing only the values of temporal and spatial weighted parameters with ADEISS implementation, solutions are implicitly obtained for the BTCS, Upwind and Crank–Nicolson schemes. The ADEISS uses iterative spreadsheet solution technique. ...

The paper demonstrates advantages of using implicit finite differences for fast, accurate, and reliable differentiating and filtering of multidimensional signals defined on regular grids. In particular, applications to image enhancement and edge detection problems are considered. The theoretical contribution of the paper is threefold. The first adapts the Fourier-Padé-Galerkin approximations ap...