Two new finite difference schemes based on the method of characteristics are presented for convection-diffusion problems. Both of the schemes are of second order in time, and the matrices of the derived systems of linear equations are symmetric. No numerical integration is required for them. The one is of first order in space and the other is of second order. For the former scheme, an optimal e...

We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and secondorder accurate in time for vanishing correlation. In our numerical study we obtain highorder numerical convergence also for non-zero correlation and non-smooth payoffs which are typical in option pricing. In all ...

This paper is concerned with the construction and developing of several nonstandard finite difference (NSFD) schemes in matrix form in order to obtain numerical solutions of epidemic models. In particular, we deal with a classical SIR epidemic model and a seasonal model associated with the evolution of the transmission of respiratory syncytial virus RSV in the human population. The first model ...

We consider the numerical integration of the Degasperis–Procesi equation, which was recently introduced as a completely integrable shallow water equation. For the equation, we propose nonlinear and linear finite difference schemes that preserve two invariants associated with the bi-Hamiltonian form of the equation at a same time. We also prove the unique solvability of the schemes, and show som...

The convergence of a class of combined spectral-finite difference methods using Hermite basis, applied to the Fokker-Planck equation, is studied. It is shown that the Hermite based spectral methods are convergent with spectral accuracy in weighted Sobolev space. Numerical results indicating the spectral convergence rate are presented. A velocity scaling factor is used in the Hermite basis and i...

The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exi...

Effects of wall material on the channel capacity of an indoor multiple input multiple output (MIMO) system are investigated using a hybrid technique of the method of moments (MoM) and the finite difference time domain (FDTD) method with consideration of the Ricean K factor and the effective degrees of freedom (EDOF) of multiple paths. key words: MIMO, channel capacity, indoor channel, hybrid me...

We study an optimal control problem for viscosity solutions of a Hamilton-Jacobi equation describing the propagation of a one dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the H−1 norm. We prove convergence of a discrete optimal control problem based on a monotone finite differenc...

Solutions of a boundary value problem for the Korteweg–de Vries equation are approximated numerically using a finite-difference method, and a collocation method based on Chebyshev polynomials. The performance of the two methods is compared using exact solutions that are exponentially small at the boundaries. The Chebyshev method is found to be more efficient. © 2009 IMACS. Published by Elsevier...

We study Soret-Dufour and radiation effects on unsteady viscous incompressible MHD flow along semi infinite inclined permeable moving plate with variable temperature and mass diffusion embedded in a porous medium numerically, by taking into account the effect of viscous dissipation. The dimensionless governing equations of flow field are solved numerically by Crank-Nicolson finite difference me...