In two-phase incompressible flow problems surface tension effects often play a key role. Due to surface tension the pressure is discontinuous across the interface. In interface capturing methods the grids are typically not aligned to the interface and thus in problems with an evolving interface time dependent pressure spaces should be used. Hence, a method of lines approach is not very suitable...

We study accuracy of alternating direction implicit (ADI) methods for parabolic equations. The original ADI method applied to parabolic equations is a perturbation of the Crank-Nicolson di erence equation and has second-order accuracy both in space and time. The perturbation error is on the same order as the discretization error, in terms of mathematical description. However, we often observe i...

The current study aimed to use the Crank-Nicolson numerical method solve Heat-Diffusion Problem in comparison with ADI method. In this paper, general formula of Numerical Method was derived and applied heat diffusion. same problem then has been solved using results were compared that revealed is more accurate than at initial steps solution.

This paper proposes the use of the Spectral method to simulate diffusive moisture transfer through porous materials, which can be strongly nonlinear and can significantly affect sensible and latent heat transfer. An alternative way for computing solutions by considering a separated representation is presented, which can be applied to both linear and nonlinear diffusive problems, considering hig...

Based on eight saul’yev asymmetry schemes and the concept of domain decomposition, a class of finite difference method (AGE) with intrinsic parallelism for 1D diffusion equations is constructed. Stability analysis for the method is done. We also pay attention to the implementation of the parallel algorithms for 2D convectiondiffusion equations. Based on another group of saul’yev asymmetry schem...

In this paper we develop two novel numerical methods for the partial integral differential equation arising from the valuation of an option whose underlying asset is governed by a jump diffusion process. These methods are based on a fitted finite volume method for the spatial discretization, an implicit-explicit time stepping scheme and the Crank-Nicolson time stepping method. We show that the ...

A novel Exponential Time Differencing (ETD) Crank-Nicolson method is developed which is stable, second order convergent, and highly efficient. We prove stability and convergence for semilinear parabolic problems with smooth data. In the nonsmooth data case we employ a positivity-preserving initial damping scheme to recover the full rate of convergence. Numerical experiments are presented for a ...

In this paper, Crank-Nicholson method for solving fractional wave equation is considered. The stability and consistency of the method are discussed by means of Greschgorin theorem and using the stability matrix analysis. Numerical solutions of some wave fractional partial differential equation models are presented. The results obtained are compared to exact solutions.

The Trapezoidal Rule with second order Backward Difference Formula (TR-BDF2) time stepping method was applied to the Black-Scholes PDE for option pricing. It is proved that TR-BDF2 time stepping method is unconditionally stable, and compared to the usual Crank-Nicolson time stepping method, the TR-BDF2 shows fewer oscillations when computing the derivatives of the solution, which are important ...

zona pellucida contains receptors for a variety of plant lectins, glycoproteins that bind to specific saccharide determinants (Oikawa, Yanagimachi & Nicol¬ son, 1973; Oikawa, Nicolson & Yanagimachi, 1974; Nicolson, Yanagimachi & Yanagimachi, 1975). Some of these lectins can bind to the zona pellucida and induce egg agglutination and/or cause changes in the ability of the exterior region of the ...